33:
202:
of all semigroups and a complete description of their structure. In the case of semigroups, since the binary operation is required to satisfy only the associativity property the problem of classification is considered extremely difficult. Descriptions of structures have been obtained for certain
210:
A (necessarily incomplete) list of various special classes of semigroups is presented below. To the extent possible the defining properties are formulated in terms of the binary operations in the semigroups. The references point to the locations from where the defining properties are sourced.
170:
of semigroups, in constructing special classes, attention is focused only on those properties, restrictions and conditions which can be expressed in terms of the binary operations in the semigroups and occasionally on the cardinality and similar properties of
203:
special classes of semigroups. For example, the structure of the sets of idempotents of regular semigroups is completely known. Structure descriptions are presented in terms of better known types of semigroups. The best known type of semigroup is the
7799:
159:
are required to satisfy not just one condition but a set of additional properties. A large collection of special classes of semigroups have been defined though not all of them have been studied equally intensively.
8841:
9031:
9541:
4043:
8897:
8746:
8548:
8293:
9483:
7452:
7331:
6243:
5882:
2310:
8943:
8640:
8594:
8339:
8038:
7973:
7717:
3754:
9396:
9314:
9262:
9178:
8128:
9225:
9141:
7644:
7569:
5830:
8383:
5744:
8405:
8150:
7493:
7372:
7251:
702:
898:
7928:
7902:
9426:
9344:
8476:
8221:
746:
57:
7731:
9905:
9883:
9785:
9761:
9698:
9595:
8754:
219:
In describing the defining properties of the various special classes of semigroups, the following notational conventions are adopted.
8970:
9810:
9620:
75:
9753:
1938:
9493:
3989:
9977:
9612:
9587:
6260:
1181:
8849:
8682:
8484:
8229:
2225:
810:
711:
48:
9449:
6393:
6196:
4202:
806:
7396:
7275:
127:
semigroups consists of all those semigroups in which the binary operation satisfies the commutativity property that
6201:
813:. Note that if this set is a variety, its set of finite elements is automatically a variety of finite semigroups.
9982:
6895:
5835:
6839:
6796:
6289:
4642:
2269:
8921:
8618:
8556:
8301:
8000:
7951:
7695:
3716:
9737:
199:
9367:
9285:
1900:
1872:
1844:
9729:
7179:
6778:
6770:
120:
9234:
9150:
8108:
9201:
9117:
7620:
7545:
9826:
9777:
9658:
6651:
3254:
1814:
1711:
1133:
617:
5799:
43:
8363:
7206:
7114:
6856:
6789:
6089:
5724:
3690:
3144:
204:
8388:
8133:
7476:
7355:
7234:
9830:
6311:
6182:
3290:
3180:
2626:
2256:
2189:
2118:
2011:
1005:
967:
680:
112:
883:
7907:
7875:
9901:
9879:
9806:
9781:
9757:
9694:
9616:
9591:
9080:
7092:
6281:
6277:
2675:
1977:
911:
290:
180:
9405:
9323:
8444:
8189:
7186:
A semigroup which is also a topological space. Such that the semigroup product is continuous.
9955:
9921:
9855:
9802:
7214:
6434:
6412:
6293:
6084:
710:
which is idempotent. This element exists, assuming the semigroup is (locally) finite. See
156:
104:
9823:
Proceedings of the
International Symposium on Theory of Regular Semigroups and Applications
2431:, group-bound semigroup, completely (or strongly) Ο-regular semigroup, and many other; see
9946:
9851:
6831:
6815:
870:
721:
198:
As in any algebraic theory, one of the main problems of the theory of semigroups is the
9575:
6558:
3094:
3089:
176:
148:
9971:
9925:
9579:
188:
17:
6782:
3950:
97:
7997:
Equivalently, for finite monoid: regular D-class are semigroup, and furthermore
7035:
6990:
3360:
3335:
3229:
1096:
1041:
152:
124:
101:
89:
848:
836:
144:
9872:
Monoids, Acts and
Categories: with Applications to Wreath Products and Graphs
9690:
6409:
184:
116:
93:
9797:
K. P. Shum "Rpp semigroups, its generalizations and special subclasses" in
7794:{\displaystyle (a^{\omega }a^{\omega }a^{\omega })^{\omega }=a^{\omega }}
2453:
2428:
809:. And whether the set of finite semigroups of this special class forms a
192:
9959:
9859:
164:
941:
172:
167:
9834:
9632:
Hui Chen (2006), "Construction of a kind of abundant semigroups",
8836:{\displaystyle a_{1}\dots a_{n}ya_{1}\dots a_{n}=a_{1}\dots a_{n}}
3372:
The direct product of a right zero semigroup and an abelian group.
3239:
The direct product of a left zero semigroup and an abelian group.
9026:{\displaystyle (a^{\omega }ba^{\omega })^{\omega }=a^{\omega }}
805:
The third column states whether this set of semigroups forms a
26:
7990:
Equivalently, regular D-class are semigroup, and furthermore
4654:
into itself with composition of mappings as binary operation.
7987:
Equivalently, every regular D-class is a rectangular band
7851:
is closed under product (i.e. this set is a subsemigroup)
3345:
The direct product of a right zero semigroup and a group.
2263:
A regular semigroup in which all idempotents are central.
9870:
Mati Kilp, Ulrich Knauer, Alexander V. Mikhalev (2000),
3342:
A semigroup which is right simple and left cancellative.
3236:
A semigroup which is left simple and right cancellative.
9669:
P. M. Edwards (1983), "Eventually regular semigroups",
9536:{\displaystyle a^{\omega }\leq a^{\omega }ba^{\omega }}
9087:
A semigroup with a partial order relation β€, such that
3367:
A right simple and conditionally commutative semigroup.
147:
semigroups consists of those semigroups for which the
9944:
Fennemore, Charles (1970), "All varieties of bands",
9496:
9452:
9408:
9370:
9326:
9288:
9237:
9204:
9153:
9120:
8973:
8924:
8852:
8757:
8685:
8621:
8559:
8487:
8447:
8391:
8366:
8304:
8232:
8192:
8136:
8111:
8003:
7954:
7910:
7878:
7734:
7698:
7623:
7548:
7479:
7399:
7358:
7278:
7237:
6204:
5838:
5802:
5727:
4038:{\displaystyle yx^{\omega }=x^{\omega }=x^{\omega }y}
3992:
3978:
Equivalently, for finite semigroup: for each element
3719:
2272:
886:
724:
683:
8892:{\displaystyle a^{\omega }ba^{\omega }=a^{\omega }}
9535:
9477:
9420:
9390:
9338:
9308:
9256:
9219:
9172:
9135:
9025:
8937:
8891:
8835:
8741:{\displaystyle ya_{1}\dots a_{n}=a_{1}\dots a_{n}}
8740:
8634:
8588:
8543:{\displaystyle ba_{1}\dots a_{n}=a_{1}\dots a_{n}}
8542:
8470:
8399:
8377:
8333:
8288:{\displaystyle a_{1}\dots a_{n}y=a_{1}\dots a_{n}}
8287:
8215:
8144:
8122:
8032:
7967:
7922:
7896:
7793:
7711:
7638:
7563:
7487:
7446:
7366:
7325:
7245:
6237:
5876:
5824:
5738:
4037:
3748:
2304:
892:
740:
696:
7099:A regular semigroup generated by its idempotents.
3295:A right zero semigroup which is a band. That is:
9478:{\displaystyle \mathbb {L} \mathbf {J} _{1}^{+}}
3786:E is countable descending chain under the order
3185:A left zero semigroup which is a band. That is:
780:an element of the semigroup such that, for each
183:are not assumed to carry any other mathematical
9848:Applications of epigroups to graded ring theory
1905:Left and right cancellative semigroup, that is
9715:Indian Journal of Pure and Applied Mathematics
9061:List of special classes of ordered semigroups
7984:Each regular D-class is an aperiodic semigroup
7447:{\displaystyle b(ab)^{\omega }=(ab)^{\omega }}
7326:{\displaystyle (ab)^{\omega }a=(ab)^{\omega }}
4564:is a nilsemigroup or a one-element semigroup.
3709:Equivalently, for finite semigroup: for each
8:
6738:Γ { 0 } Γ Ξ ) is the Rees matrix semigroup
6238:{\displaystyle \langle x,y\mid xy=1\rangle }
6232:
6205:
1292:Left and right weakly commutative. That is:
9927:Mathematical Foundations of Automata Theory
9671:Bulletin of Australian Mathematical Society
7804:Equivalently, regular H-classes are groups,
5877:{\displaystyle (aba)^{\omega }=a^{\omega }}
9609:The Algebraic Theory of Semigroups Vol. II
9053:
1484:-commutative and conditionally commutative
1427:-commutative and conditionally commutative
815:
714:for more information about this notation.
9584:The Algebraic Theory of Semigroups Vol. I
9527:
9514:
9501:
9495:
9469:
9464:
9459:
9454:
9453:
9451:
9407:
9382:
9377:
9372:
9369:
9325:
9300:
9295:
9290:
9287:
9242:
9236:
9211:
9206:
9203:
9164:
9152:
9127:
9122:
9119:
9017:
9004:
8994:
8981:
8972:
8930:
8926:
8925:
8923:
8883:
8870:
8857:
8851:
8827:
8814:
8801:
8788:
8775:
8762:
8756:
8732:
8719:
8706:
8693:
8684:
8627:
8623:
8622:
8620:
8580:
8567:
8558:
8534:
8521:
8508:
8495:
8486:
8461:
8453:
8452:
8446:
8392:
8390:
8367:
8365:
8325:
8309:
8303:
8279:
8266:
8250:
8237:
8231:
8206:
8198:
8197:
8191:
8137:
8135:
8115:
8110:
8024:
8011:
8002:
7960:
7956:
7955:
7953:
7909:
7888:
7883:
7877:
7854:Equivalently, there exists no idempotent
7785:
7772:
7762:
7752:
7742:
7733:
7704:
7700:
7699:
7697:
7629:
7624:
7622:
7554:
7549:
7547:
7480:
7478:
7438:
7416:
7398:
7359:
7357:
7317:
7292:
7277:
7238:
7236:
6203:
5868:
5855:
5837:
5807:
5801:
5728:
5726:
4296:Every finitely generated subsemigroup of
4026:
4013:
4000:
3991:
3740:
3724:
3718:
2305:{\displaystyle a^{\omega }b=ba^{\omega }}
2296:
2277:
2271:
1773:depending on the couple (a,b) such that (
885:
733:
725:
723:
688:
682:
76:Learn how and when to remove this message
9709:K. S. Harinath (1979), "Some results on
8938:{\displaystyle \mathbb {L} \mathbf {G} }
8635:{\displaystyle \mathbb {L} \mathbf {1} }
8589:{\displaystyle ba^{\omega }=a^{\omega }}
8334:{\displaystyle a^{\omega }b=a^{\omega }}
8033:{\displaystyle aa^{\omega }=a^{\omega }}
7968:{\displaystyle \mathbb {D} \mathbf {A} }
7712:{\displaystyle \mathbb {D} \mathbf {S} }
6955:Semigroup of one-to-one transformations
3749:{\displaystyle a^{\omega }a=a^{\omega }}
221:
9640:), 165β171 (Accessed on 25 April 2009)
9068:
6573:Set of finite sequences of elements of
4272:is equal to the semigroup generated by
2975:(Right principal projective semigroup)
824:
9854:, Volume 50, Number 1 (1995), 327-350
9607:A. H. Clifford, G. B. Preston (1967).
3033:(Left principal projective semigroup)
817:List of special classes of semigroups
9799:Advances in Algebra and Combinatorics
9485:locally positive J-trivial semigroup
7213:The smallest finite monoid which can
4115:is an ideal, a nilsemigroup, and 0 β
801:List of special classes of semigroups
7:
9391:{\displaystyle \mathbf {J} _{1}^{-}}
9309:{\displaystyle \mathbf {J} _{1}^{+}}
8967:Equivalently, for finite semigroup:
8846:Equivalently, for finite semigroup:
8751:Equivalently, for finite semigroup:
8679:Equivalently, for finite semigroup:
8553:Equivalently, for finite semigroup:
8481:Equivalently, for finite semigroup:
8437:Equivalently, for finite semigroup:
8298:Equivalently, for finite semigroup:
8226:Equivalently, for finite semigroup:
8182:Equivalently, for finite semigroup:
7515:Equivalently, the monoids which are
7272:Equivalently, for finite semigroup:
5796:equivalently, for finite semigroup:
4245:is the only congruence contained in
2266:Equivalently, for finite semigroup:
1345:Conditionally commutative semigroup
8430:is a right zero semigroup equal to
3075:, contains at least one idempotent.
3017:, contains at least one idempotent.
9801:edited by K P Shum et al. (2008),
9231:Nilpotent finite semigroups, with
9147:Nilpotent finite semigroups, with
8175:is a left zero semigroup equal to
7830:Equivalently, for each idempotent
7728:Equivalently, for finite monoids:
7665:Equivalently, for finite monoids:
7590:Equivalently, for finite monoids:
7393:Equivalently, for finite monoids,
887:
25:
9772:M. Petrich, N. R. Reilly (1999).
9257:{\displaystyle b^{\omega }\leq a}
9173:{\displaystyle a\leq b^{\omega }}
8441:is a right zero semigroup equals
8123:{\displaystyle \ell \mathbf {1} }
1613:Externally commutative semigroup
123:or conditions. Thus the class of
9734:Fundamentals of Semigroup Theory
9460:
9373:
9291:
9220:{\displaystyle \mathbf {N} ^{-}}
9207:
9136:{\displaystyle \mathbf {N} ^{+}}
9123:
8931:
8628:
8393:
8371:
8368:
8186:is a left zero semigroup equals
8138:
8116:
7961:
7705:
7639:{\displaystyle \mathbf {L_{1}} }
7630:
7626:
7564:{\displaystyle \mathbf {R_{1}} }
7555:
7551:
7481:
7360:
7239:
5732:
5729:
2566:Strongly unit regular semigroup
31:
9095:implies cβ’a β€ cβ’b and aβ’c β€ bβ’c
7045:There exists a unary operation
7000:There exists a unary operation
6982:
6904:There exists a unary operation
4264:Idempotent generated semigroup
3903:Complete commutative semigroup
143:in the semigroup. The class of
9898:Techniques of semigroup theory
9001:
8974:
8462:
8454:
8207:
8199:
7769:
7735:
7662:-equivalence class is trivial.
7587:-equivalence class is trivial.
7512:-equivalence class is trivial.
7435:
7425:
7413:
7403:
7390:-equivalence class is trivial.
7314:
7304:
7289:
7279:
7269:-equivalence class is trivial.
7217:a subset of another semigroup.
6378:are equal, all four are equal.
6350:
5852:
5839:
5825:{\displaystyle a^{\omega }a=a}
5503:Completely 0-simple semigroup
3328:
3220:
2218:
2147:
2040:
1087:
1034:
734:
726:
1:
9878:, Walter de Gruyter, Berlin,
9874:, Expositions in Mathematics
9774:Completely regular semigroups
9750:Special Classes of Semigroups
9613:American Mathematical Society
9588:American Mathematical Society
9490:Finite semigroups satisfying
8378:{\displaystyle \mathbf {r1} }
6261:Full transformation semigroup
5739:{\displaystyle \mathbf {CS} }
5691:. Each Rees factor semigroup
4643:Full transformation semigroup
4560:is a cancellative semigroup,
4193:Finitely presented semigroup
1182:Nowhere commutative semigroup
1046:A commutative band, that is:
9660:(Accessed on 27 April 2009)
8642:: Locally trivial semigroup
8400:{\displaystyle \mathbf {D} }
8145:{\displaystyle \mathbf {K} }
7488:{\displaystyle \mathbf {J} }
7367:{\displaystyle \mathbf {L} }
7246:{\displaystyle \mathbf {R} }
6848:
6806:
6761:
6550:
6426:
6385:
6303:
6252:
6174:
6134:
6076:
6024:
5972:
5898:
5714:
5638:
5602:
5495:
5416:Completely simple semigroup
5408:
5371:
4721:Right unambiguous semigroup
4713:
4661:
3682:
3655:
3628:
3591:
3553:
3490:
3450:
3410:
3352:
3282:
3246:
3172:
3136:
2872:
2709:
2523:
2372:Eventually regular semigroup
2226:Completely regular semigroup
2181:
2110:
2078:
2003:
1969:
1930:
1892:
1864:
1845:Right cancellative semigroup
1769:There is a positive integer
1561:Right commutative semigroup
1530:Quasi-commutative semigroup
1209:
1173:
1125:
1081:
997:
828:Variety of finite semigroup
811:variety of finite semigroups
764:For example, the definition
712:variety of finite semigroups
400:Arbitrary positive integers
9900:. Oxford University Press.
9634:Mathematical Communications
6394:Symmetric inverse semigroup
4784:Left unambiguous semigroup
4669:Weakly reductive semigroup
3636:Right reversible semigroup
1873:Left cancellative semigroup
1587:Left commutative semigroup
697:{\displaystyle x^{\omega }}
414:Specific positive integers
109:special class of semigroups
51:. The specific problem is:
9999:
9937:
9914:
9889:
9864:
9840:
9816:
9790:
9766:
9742:
9723:
9703:
9679:
9663:
9643:
9625:
9600:
9569:
8407:: Right trivial semigroup
8152:: Lefty trivial semigroup
7975:: Semigroup whose regular
7719:: Semigroup whose regular
6871:= { 0,1,2, ... } under + .
5324:for some positive integer
4400:(Right inverse semigroup)
3663:Left reversible semigroup
3458:Right reductive semigroup
2795:(Pseudoinverse semigroup)
2793:Locally inverse semigroup
2427:Quasi-periodic semigroup,
893:{\displaystyle \emptyset }
155:. Members of the class of
47:to meet Knowledge (XXG)'s
9896:Peter M. Higgins (1992).
7923:{\displaystyle S\times S}
7897:{\displaystyle B_{2}^{1}}
7872:Equivalently, the monoid
7106:
7084:
7027:
6943:
6896:Semigroup with involution
6888:
6642:
6539:β 0 ) β
6481:β 0 ) β
6463:β 0 ) β
6032:Right 0-simple semigroup
5904:
5334:
5284:
5239:
5197:
5084:
5016:
4948:
4839:
4776:
4631:
4523:
4492:
4461:
4437:(Left inverse semigroup)
4424:
4387:
4315:
4291:Locally finite semigroup
4283:
4256:
4228:
4185:
4125:
4059:
3942:
3931:Every nonempty subset of
3896:
3860:
3833:
3805:
3418:Left reductive semigroup
3379:
3082:
3024:
2966:
2825:
2785:
2747:
2667:
2662:
2475:
2470:
2466:
2432:
2419:
2415:
2411:
2376:Quasi regular semigroup)
2365:
2247:
1939:''E''-inversive semigroup
1836:
1805:
1748:
1703:
1657:
1631:
1605:
1579:
1553:
1522:
1491:
1465:
1434:
1408:
1377:
1337:
1281:
1253:Right weakly commutative
1245:
959:
670:Green classes containing
9554:
9439:
9357:
9275:
9191:
9107:
9045:
8911:
8608:
8353:
8098:
7979:are aperiodic semigroup
7941:
7685:
7658:-trivial. That is, each
7610:
7583:-trivial. That is, each
7535:
7508:-trivial. That is, each
7466:
7386:-trivial. That is, each
7345:
7265:-trivial. That is, each
7224:
7198:
6797:composition of functions
6159:, ... } is a finite set.
5980:Left 0-simple semigroup
5910:
5707:) is 0-simple or simple.
5092:0-unambiguous semigroup
4531:Subelementary semigroup
4065:
3840:Right Clifford semigroup
3771:
3765:
2619:
2559:
2323:
2154:Right regular semigroup
2047:Intra-regular semigroup
1217:Left weakly commutative
9738:Oxford University Press
9421:{\displaystyle a\leq 1}
9339:{\displaystyle 1\leq a}
8471:{\displaystyle S^{|S|}}
8216:{\displaystyle S^{|S|}}
6683:Define an operation in
6492:β 0 there exist unique
6413:partial transformations
6290:composition of mappings
5247:Right Putcha semigroup
4650:Set of all mappings of
4500:Right simple semigroup
4344:and a positive integer
3813:Left Clifford semigroup
2818:is a pseudosemilattice.
2755:Right inverse semigroup
2717:Left inverse semigroup
2531:Unit regular semigroup
2086:Left regular semigroup
1502:-commutative semigroup
1476:-commutative semigroup
1445:-commutative semigroup
1419:-commutative semigroup
1388:-commutative semigroup
971:(Idempotent semigroup)
9713:-regular semigroups",
9685:P. A. Grillet (1995).
9537:
9479:
9422:
9392:
9340:
9310:
9258:
9221:
9174:
9137:
9027:
8939:
8893:
8837:
8742:
8636:
8590:
8544:
8472:
8401:
8379:
8335:
8289:
8217:
8146:
8124:
8034:
7969:
7924:
7898:
7795:
7713:
7640:
7565:
7489:
7448:
7368:
7327:
7247:
6779:linear transformations
6771:linear transformations
6357:Rectangular semigroup
6272:(Symmetric semigroup)
6239:
5878:
5826:
5740:
5559:There exists non-zero
5205:Left Putcha semigroup
4847:Unambiguous semigroup
4469:Left simple semigroup
4236:Fundamental semigroup
4039:
3953:(Nilpotent semigroup)
3750:
2959:, contain idempotents.
2374:(Ο-regular semigroup,
2306:
1901:Cancellative semigroup
1136:commutative semigroup
894:
742:
698:
428:Arbitrary elements of
366:Arbitrary elements of
324:Arbitrary elements of
251:Set of idempotents in
119:satisfying additional
9778:John Wiley & Sons
9538:
9480:
9423:
9393:
9341:
9311:
9259:
9222:
9175:
9138:
9028:
8940:
8894:
8838:
8743:
8637:
8591:
8545:
8473:
8402:
8380:
8336:
8290:
8218:
8147:
8125:
8035:
7970:
7925:
7899:
7796:
7714:
7641:
7566:
7490:
7449:
7369:
7328:
7248:
7180:Topological semigroup
7125:such that for all a,
6240:
5879:
5827:
5741:
5646:Semisimple semigroup
5615:(Bisimple semigroup)
5379:0-bisimple semigroup
4435:-unipotent semigroup
4398:-unipotent semigroup
4075:Elementary semigroup
4040:
3967:= 0 for some integer
3886:is a subsemigroup of
3751:
3599:Reversible semigroup
3561:Separative semigroup
2836:-inversive semigroup
2651:is a subsemigroup of
2307:
895:
743:
699:
345:Specific elements of
18:Commutative semigroup
9978:Algebraic structures
9827:University of Kerala
9748:Attila Nagy (2001).
9655:Numerical semigroups
9494:
9450:
9406:
9368:
9324:
9286:
9235:
9202:
9151:
9118:
8971:
8922:
8850:
8755:
8683:
8619:
8557:
8485:
8445:
8389:
8364:
8302:
8230:
8190:
8134:
8109:
8001:
7952:
7908:
7876:
7732:
7696:
7621:
7546:
7477:
7397:
7356:
7276:
7235:
6950:BaerβLevi semigroup
6202:
5836:
5800:
5725:
5024:Right 0-unambiguous
4141:There exists unique
4106:is a group, and 1 β
3990:
3920:is in a subgroup of
3717:
3498:Reductive semigroup
3387:Unipotent semigroup
3255:Right zero semigroup
2682:There exists unique
2483:Primitive semigroup
2334:-regular semigroup (
2270:
884:
722:
681:
450:Identity element of
379:Specific element of
241:Arbitrary semigroup
58:improve this article
9813:(pp. 303β334)
9474:
9387:
9305:
9062:
7893:
7207:Syntactic semigroup
6857:Numerical semigroup
6142:Periodic semigroup
6090:Monogenic semigroup
5920:0-simple semigroup
5761:. (There exists no
5746:: Simple semigroup
5567:such that whenever
5464:such that whenever
5348:-simple semigroup)
4956:Left 0-unambiguous
4639:Symmetric semigroup
4371: β
4136:-unitary semigroup
3691:Aperiodic semigroup
3577: β
3361:Right abelian group
3145:Left zero semigroup
2880:Abundant semigroup
1882: β
1854: β
1289:Weakly commutative
818:
772:should be read as:
750:The cardinality of
741:{\displaystyle |X|}
224:
9960:10.1007/BF02573031
9860:10.1007/BF02573530
9831:Thiruvananthapuram
9611:(Second Edition).
9586:(Second Edition).
9533:
9475:
9458:
9418:
9402:Semilattices with
9388:
9371:
9336:
9320:Semilattices with
9306:
9289:
9254:
9217:
9170:
9133:
9069:Defining property
9060:
9023:
8935:
8889:
8833:
8738:
8632:
8586:
8540:
8468:
8397:
8375:
8331:
8285:
8213:
8142:
8120:
8030:
7965:
7944:pp. 154, 155, 158
7920:
7894:
7879:
7791:
7709:
7636:
7561:
7504:Monoids which are
7485:
7444:
7364:
7323:
7243:
6577:with the operation
6362:Whenever three of
6235:
6183:Bicyclic semigroup
5874:
5822:
5736:
5342:Bisimple semigroup
4450:contains a unique
4413:contains a unique
4035:
3746:
2774:contains a unique
2736:contains a unique
2627:Orthodox semigroup
2302:
2257:Clifford semigroup
2190:Right-regular band
1945:-dense semigroup)
890:
825:Defining property
816:
788:in the semigroup,
738:
706:The only power of
694:
264:Group of units in
222:
179:. The underlying
53:various, see talk.
9966:
9965:
9907:978-0-19-853577-5
9884:978-3-11-015248-7
9786:978-0-471-19571-9
9762:978-0-7923-6890-8
9699:978-0-8247-9662-4
9596:978-0-8218-0272-4
9561:
9560:
9081:Ordered semigroup
9059:
9052:
9051:
8945:: Locally groups
7650:-trivial monoids
7646:: idempotent and
7575:-trivial monoids
7571:: idempotent and
7499:-trivial monoids
7378:-trivial monoids
7257:-trivial monoids
6408:The semigroup of
6318:A band such that
6288:into itself with
6112:, ... } for some
5613:-simple semigroup
5292:Putcha semigroup
4362: β
3971:which depends on
3706:) such that a = a
2676:Inverse semigroup
2196:A band such that
2125:A band such that
2119:Left-regular band
2018:A band such that
1978:Regular semigroup
1920: β
1911: β
1639:Medial semigroup
1012:A band such that
912:Trivial semigroup
762:
761:
618:Green's relations
277:Minimal ideal of
157:Brandt semigroups
135:for all elements
100:together with an
86:
85:
78:
49:quality standards
40:This article may
16:(Redirected from
9990:
9983:Semigroup theory
9962:
9934:
9932:
9911:
9803:World Scientific
9720:(11), 1422β1431
9568:
9567:
9542:
9540:
9539:
9534:
9532:
9531:
9519:
9518:
9506:
9505:
9484:
9482:
9481:
9476:
9473:
9468:
9463:
9457:
9427:
9425:
9424:
9419:
9397:
9395:
9394:
9389:
9386:
9381:
9376:
9345:
9343:
9342:
9337:
9315:
9313:
9312:
9307:
9304:
9299:
9294:
9263:
9261:
9260:
9255:
9247:
9246:
9226:
9224:
9223:
9218:
9216:
9215:
9210:
9179:
9177:
9176:
9171:
9169:
9168:
9142:
9140:
9139:
9134:
9132:
9131:
9126:
9063:
9054:
9032:
9030:
9029:
9024:
9022:
9021:
9009:
9008:
8999:
8998:
8986:
8985:
8944:
8942:
8941:
8936:
8934:
8929:
8898:
8896:
8895:
8890:
8888:
8887:
8875:
8874:
8862:
8861:
8842:
8840:
8839:
8834:
8832:
8831:
8819:
8818:
8806:
8805:
8793:
8792:
8780:
8779:
8767:
8766:
8747:
8745:
8744:
8739:
8737:
8736:
8724:
8723:
8711:
8710:
8698:
8697:
8641:
8639:
8638:
8633:
8631:
8626:
8595:
8593:
8592:
8587:
8585:
8584:
8572:
8571:
8549:
8547:
8546:
8541:
8539:
8538:
8526:
8525:
8513:
8512:
8500:
8499:
8477:
8475:
8474:
8469:
8467:
8466:
8465:
8457:
8406:
8404:
8403:
8398:
8396:
8384:
8382:
8381:
8376:
8374:
8340:
8338:
8337:
8332:
8330:
8329:
8314:
8313:
8294:
8292:
8291:
8286:
8284:
8283:
8271:
8270:
8255:
8254:
8242:
8241:
8222:
8220:
8219:
8214:
8212:
8211:
8210:
8202:
8151:
8149:
8148:
8143:
8141:
8129:
8127:
8126:
8121:
8119:
8039:
8037:
8036:
8031:
8029:
8028:
8016:
8015:
7974:
7972:
7971:
7966:
7964:
7959:
7929:
7927:
7926:
7921:
7904:does not divide
7903:
7901:
7900:
7895:
7892:
7887:
7800:
7798:
7797:
7792:
7790:
7789:
7777:
7776:
7767:
7766:
7757:
7756:
7747:
7746:
7718:
7716:
7715:
7710:
7708:
7703:
7645:
7643:
7642:
7637:
7635:
7634:
7633:
7570:
7568:
7567:
7562:
7560:
7559:
7558:
7494:
7492:
7491:
7486:
7484:
7453:
7451:
7450:
7445:
7443:
7442:
7421:
7420:
7373:
7371:
7370:
7365:
7363:
7332:
7330:
7329:
7324:
7322:
7321:
7297:
7296:
7252:
7250:
7249:
7244:
7242:
6832:binary relations
6816:binary relations
6666:with 0 adjoined.
6435:Brandt semigroup
6312:Rectangular band
6294:binary operation
6244:
6242:
6241:
6236:
6085:Cyclic semigroup
5883:
5881:
5880:
5875:
5873:
5872:
5860:
5859:
5831:
5829:
5828:
5823:
5812:
5811:
5745:
5743:
5742:
5737:
5735:
5421:There exists no
5310: β
5262: β
5217: β
5165: β
5120: β
5052: β
4984: β
4171: β
4044:
4042:
4041:
4036:
4031:
4030:
4018:
4017:
4005:
4004:
3808:p. 233β238
3755:
3753:
3752:
3747:
3745:
3744:
3729:
3728:
3594:p. 130β131
2311:
2309:
2308:
2303:
2301:
2300:
2282:
2281:
1195: β
1006:Rectangular band
899:
897:
896:
891:
819:
747:
745:
744:
739:
737:
729:
703:
701:
700:
695:
693:
692:
439:Zero element of
225:
105:binary operation
81:
74:
70:
67:
61:
35:
34:
27:
21:
9998:
9997:
9993:
9992:
9991:
9989:
9988:
9987:
9968:
9967:
9947:Semigroup Forum
9943:
9930:
9920:
9908:
9895:
9852:Semigroup Forum
9846:A. V. Kelarev,
9566:
9523:
9510:
9497:
9492:
9491:
9448:
9447:
9404:
9403:
9366:
9365:
9322:
9321:
9284:
9283:
9238:
9233:
9232:
9205:
9200:
9199:
9160:
9149:
9148:
9121:
9116:
9115:
9013:
9000:
8990:
8977:
8969:
8968:
8920:
8919:
8879:
8866:
8853:
8848:
8847:
8823:
8810:
8797:
8784:
8771:
8758:
8753:
8752:
8728:
8715:
8702:
8689:
8681:
8680:
8617:
8616:
8576:
8563:
8555:
8554:
8530:
8517:
8504:
8491:
8483:
8482:
8448:
8443:
8442:
8387:
8386:
8362:
8361:
8321:
8305:
8300:
8299:
8275:
8262:
8246:
8233:
8228:
8227:
8193:
8188:
8187:
8132:
8131:
8107:
8106:
8074:
8051:
8020:
8007:
7999:
7998:
7950:
7949:
7906:
7905:
7874:
7873:
7847:
7816:
7781:
7768:
7758:
7748:
7738:
7730:
7729:
7694:
7693:
7625:
7619:
7618:
7550:
7544:
7543:
7475:
7474:
7434:
7412:
7395:
7394:
7354:
7353:
7313:
7288:
7274:
7273:
7233:
7232:
6898:
6825:
6634:
6627:
6620:
6613:
6606:
6599:
6592:
6585:
6578:
6568:
6403:
6271:
6270:
6200:
6199:
6087:
5864:
5851:
5834:
5833:
5803:
5798:
5797:
5755:
5723:
5722:
5690:
5627:
5614:
5360:
5343:
5187:
5174:
5157:
5142:
5129:
5112:
5074:
5061:
5044:
5006:
4993:
4976:
4937:
4924:
4911:
4891:
4878:
4865:
4828:
4815:
4802:
4765:
4752:
4739:
4640:
4512:
4481:
4449:
4436:
4412:
4399:
4092:is of the form
4022:
4009:
3996:
3988:
3987:
3935:has an infimum.
3879:
3842:(RC-semigroup)
3841:
3815:(LC-semigroup)
3814:
3795:
3736:
3720:
3715:
3714:
3693:
3355:p. 37, 38
3291:Right zero band
3249:p. 37, 38
3092:
3047:
3032:
2989:
2974:
2904:
2894:
2794:
2773:
2756:
2735:
2718:
2666:
2474:
2469:
2418:
2414:
2375:
2373:
2292:
2273:
2268:
2267:
2239:
1494:p. 93β107
1437:p. 93β107
970:
918:Cardinality of
882:
881:
871:Empty semigroup
803:
720:
719:
684:
679:
678:
667:
658:
649:
640:
631:
578:
556:
548:
529:
520:
516:
507:
503:
494:
490:
474:βͺ { 1 } if 1 β
217:
82:
71:
65:
62:
55:
36:
32:
23:
22:
15:
12:
11:
5:
9996:
9994:
9986:
9985:
9980:
9970:
9969:
9964:
9963:
9954:(1): 172β179,
9941:
9939:
9936:
9935:
9924:(2016-11-30).
9922:Pin, Jean-Γric
9918:
9916:
9913:
9912:
9906:
9893:
9891:
9888:
9887:
9868:
9866:
9863:
9862:
9844:
9842:
9839:
9838:
9820:
9818:
9815:
9814:
9795:
9793:
9792:
9789:
9788:
9770:
9768:
9765:
9764:
9746:
9744:
9741:
9740:
9727:
9725:
9722:
9721:
9707:
9705:
9702:
9701:
9683:
9681:
9678:
9677:
9667:
9665:
9662:
9661:
9647:
9645:
9642:
9641:
9630:
9628:
9624:
9623:
9605:
9603:
9599:
9598:
9576:A. H. Clifford
9573:
9571:
9565:
9562:
9559:
9558:
9552:
9551:
9550:
9545:
9544:
9543:
9530:
9526:
9522:
9517:
9513:
9509:
9504:
9500:
9486:
9472:
9467:
9462:
9456:
9444:
9443:
9437:
9436:
9435:
9430:
9429:
9428:
9417:
9414:
9411:
9398:
9385:
9380:
9375:
9362:
9361:
9355:
9354:
9353:
9348:
9347:
9346:
9335:
9332:
9329:
9316:
9303:
9298:
9293:
9280:
9279:
9273:
9272:
9271:
9266:
9265:
9264:
9253:
9250:
9245:
9241:
9227:
9214:
9209:
9196:
9195:
9189:
9188:
9187:
9182:
9181:
9180:
9167:
9163:
9159:
9156:
9143:
9130:
9125:
9112:
9111:
9105:
9104:
9103:
9098:
9097:
9096:
9083:
9077:
9076:
9073:
9070:
9067:
9058:
9057:
9050:
9049:
9043:
9042:
9041:
9036:
9035:
9034:
9020:
9016:
9012:
9007:
9003:
8997:
8993:
8989:
8984:
8980:
8976:
8965:
8956:Equivalently,
8954:
8946:
8933:
8928:
8916:
8915:
8909:
8908:
8907:
8902:
8901:
8900:
8886:
8882:
8878:
8873:
8869:
8865:
8860:
8856:
8844:
8830:
8826:
8822:
8817:
8813:
8809:
8804:
8800:
8796:
8791:
8787:
8783:
8778:
8774:
8770:
8765:
8761:
8749:
8735:
8731:
8727:
8722:
8718:
8714:
8709:
8705:
8701:
8696:
8692:
8688:
8677:
8668:Equivalently,
8666:
8657:Equivalently,
8655:
8643:
8630:
8625:
8613:
8612:
8606:
8605:
8604:
8599:
8598:
8597:
8583:
8579:
8575:
8570:
8566:
8562:
8551:
8537:
8533:
8529:
8524:
8520:
8516:
8511:
8507:
8503:
8498:
8494:
8490:
8479:
8464:
8460:
8456:
8451:
8435:
8426:Equivalently,
8424:
8408:
8395:
8373:
8370:
8358:
8357:
8351:
8350:
8349:
8344:
8343:
8342:
8328:
8324:
8320:
8317:
8312:
8308:
8296:
8282:
8278:
8274:
8269:
8265:
8261:
8258:
8253:
8249:
8245:
8240:
8236:
8224:
8209:
8205:
8201:
8196:
8180:
8171:Equivalently,
8169:
8153:
8140:
8118:
8114:
8103:
8102:
8096:
8095:
8094:
8089:
8088:
8087:
8070:
8065:Equivalently,
8063:
8047:
8042:Equivalently,
8040:
8027:
8023:
8019:
8014:
8010:
8006:
7995:
7988:
7985:
7980:
7963:
7958:
7946:
7945:
7939:
7938:
7937:
7932:
7931:
7930:
7919:
7916:
7913:
7891:
7886:
7882:
7870:
7852:
7843:
7828:
7812:
7807:Equivalently,
7805:
7802:
7788:
7784:
7780:
7775:
7771:
7765:
7761:
7755:
7751:
7745:
7741:
7737:
7724:
7723:are semigroup
7707:
7702:
7690:
7689:
7683:
7682:
7681:
7676:
7675:
7674:
7663:
7651:
7632:
7628:
7615:
7614:
7608:
7607:
7606:
7601:
7600:
7599:
7588:
7576:
7557:
7553:
7540:
7539:
7533:
7532:
7531:
7526:
7525:
7524:
7513:
7500:
7483:
7471:
7470:
7464:
7463:
7462:
7457:
7456:
7455:
7441:
7437:
7433:
7430:
7427:
7424:
7419:
7415:
7411:
7408:
7405:
7402:
7391:
7379:
7362:
7350:
7349:
7343:
7342:
7341:
7336:
7335:
7334:
7320:
7316:
7312:
7309:
7306:
7303:
7300:
7295:
7291:
7287:
7284:
7281:
7270:
7258:
7241:
7229:
7228:
7222:
7220:
7219:
7218:
7209:
7203:
7202:
7196:
7195:
7194:
7193:Not applicable
7189:
7188:
7187:
7182:
7176:
7175:
7173:
7172:
7171:
7168:
7163:
7162:
7161:
7144:(depending on
7138:
7117:
7111:
7110:
7104:
7102:
7101:
7100:
7095:
7089:
7088:
7082:
7080:
7079:
7078:
7041:
7032:
7031:
7025:
7023:
7022:
7021:
6996:
6987:
6986:
6980:
6978:
6977:
6976:
6975:) is infinite.
6951:
6947:
6946:
6941:
6939:
6938:
6937:
6900:
6899:(*-semigroup)
6892:
6891:
6886:
6884:
6883:
6882:
6872:
6859:
6853:
6852:
6846:
6844:
6843:
6842:
6826:
6821:
6811:
6810:
6804:
6802:
6801:
6800:
6773:
6766:
6765:
6759:
6757:
6756:
6755:
6724:
6681:
6667:
6655:
6647:
6646:
6640:
6638:
6637:
6636:
6632:
6625:
6618:
6611:
6604:
6597:
6590:
6583:
6569:
6564:
6559:Free semigroup
6555:
6554:
6548:
6546:
6545:
6544:
6529:
6486:
6471:
6445:
6437:
6431:
6430:
6424:
6422:
6421:
6420:
6404:
6399:
6390:
6389:
6383:
6381:
6380:
6379:
6358:
6354:
6353:
6348:
6347:
6346:
6343:
6338:
6337:
6336:
6326:
6314:
6308:
6307:
6301:
6299:
6298:
6297:
6273:
6266:
6257:
6256:
6255:p. 43β46
6250:
6248:
6247:
6246:
6234:
6231:
6228:
6225:
6222:
6219:
6216:
6213:
6210:
6207:
6190:
6185:
6179:
6178:
6172:
6171:
6170:
6167:
6162:
6161:
6160:
6143:
6139:
6138:
6132:
6131:
6130:
6127:
6122:
6121:
6120:
6093:
6081:
6080:
6074:
6072:
6071:
6070:
6047:
6041:
6033:
6029:
6028:
6022:
6020:
6019:
6018:
6005:is such that
5995:
5989:
5981:
5977:
5976:
5970:
5968:
5967:
5966:
5935:
5929:
5921:
5917:
5916:
5915:
5914:
5908:
5902:
5894:
5893:
5892:
5887:
5886:
5885:
5871:
5867:
5863:
5858:
5854:
5850:
5847:
5844:
5841:
5821:
5818:
5815:
5810:
5806:
5794:
5753:
5747:
5734:
5731:
5719:
5718:
5717:p. 71β75
5712:
5710:
5709:
5708:
5686:
5647:
5643:
5642:
5636:
5634:
5633:
5632:
5623:
5616:
5607:
5606:
5600:
5598:
5597:
5596:
5557:
5518:
5512:
5504:
5500:
5499:
5493:
5491:
5490:
5489:
5454:
5417:
5413:
5412:
5406:
5404:
5403:
5402:
5388:
5380:
5376:
5375:
5369:
5367:
5366:
5365:
5356:
5349:
5339:
5338:
5332:
5330:
5329:
5328:
5293:
5289:
5288:
5282:
5280:
5279:
5278:
5248:
5244:
5243:
5237:
5235:
5234:
5233:
5206:
5202:
5201:
5195:
5193:
5192:
5191:
5183:
5170:
5153:
5146:
5138:
5125:
5108:
5101:
5093:
5089:
5088:
5082:
5080:
5079:
5078:
5070:
5057:
5040:
5033:
5025:
5021:
5020:
5014:
5012:
5011:
5010:
5002:
4989:
4972:
4965:
4957:
4953:
4952:
4946:
4944:
4943:
4942:
4933:
4920:
4907:
4896:
4887:
4874:
4861:
4848:
4844:
4843:
4837:
4835:
4834:
4833:
4824:
4811:
4798:
4785:
4781:
4780:
4774:
4772:
4771:
4770:
4761:
4748:
4735:
4722:
4718:
4717:
4711:
4709:
4708:
4707:
4670:
4666:
4665:
4659:
4657:
4656:
4655:
4646:
4636:
4635:
4629:
4627:
4626:
4625:
4586:
4575:
4565:
4543:
4532:
4528:
4527:
4521:
4519:
4518:
4517:
4508:
4501:
4497:
4496:
4490:
4488:
4487:
4486:
4477:
4470:
4466:
4465:
4459:
4457:
4456:
4455:
4445:
4438:
4429:
4428:
4422:
4420:
4419:
4418:
4408:
4401:
4392:
4391:
4385:
4383:
4382:
4381:
4375:
4366:
4357:
4338:
4327:
4320:
4319:
4313:
4312:
4311:
4308:
4303:
4302:
4301:
4292:
4288:
4287:
4281:
4279:
4278:
4277:
4265:
4261:
4260:
4254:
4252:
4251:
4250:
4237:
4233:
4232:
4226:
4224:
4223:
4222:
4194:
4190:
4189:
4183:
4181:
4180:
4179:
4162:
4137:
4130:
4129:
4123:
4121:
4120:
4119:
4110:
4101:
4087:
4076:
4072:
4071:
4070:
4069:
4063:
4055:
4054:
4053:
4048:
4047:
4046:
4034:
4029:
4025:
4021:
4016:
4012:
4008:
4003:
3999:
3995:
3976:
3962:
3954:
3947:
3946:
3940:
3938:
3937:
3936:
3929:
3915:
3904:
3900:
3899:
3894:
3892:
3891:
3890:
3881:
3875:
3868:
3864:
3863:
3858:
3856:
3855:
3854:
3843:
3837:
3836:
3831:
3829:
3828:
3827:
3816:
3810:
3809:
3803:
3801:
3800:
3799:
3791:
3782:
3778:
3777:
3776:
3775:
3769:
3761:
3759:
3758:
3757:
3743:
3739:
3735:
3732:
3727:
3723:
3707:
3702:(depending on
3694:
3687:
3686:
3680:
3678:
3677:
3676:
3664:
3660:
3659:
3653:
3651:
3650:
3649:
3637:
3633:
3632:
3626:
3624:
3623:
3622:
3612:
3600:
3596:
3595:
3589:
3587:
3586:
3585:
3562:
3558:
3557:
3551:
3549:
3548:
3547:
3524:
3499:
3495:
3494:
3488:
3486:
3485:
3484:
3459:
3455:
3454:
3448:
3446:
3445:
3444:
3419:
3415:
3414:
3408:
3407:
3406:
3403:
3398:
3397:
3396:
3388:
3384:
3383:
3377:
3375:
3374:
3373:
3369:
3368:
3363:
3357:
3356:
3350:
3348:
3347:
3346:
3343:
3338:
3332:
3331:
3326:
3325:
3324:
3321:
3316:
3315:
3314:
3305:
3293:
3287:
3286:
3280:
3279:
3278:
3275:
3270:
3269:
3268:
3257:
3251:
3250:
3244:
3242:
3241:
3240:
3237:
3232:
3226:
3225:
3224:
3223:
3216:
3215:
3214:
3211:
3206:
3205:
3204:
3195:
3183:
3181:Left zero band
3177:
3176:
3170:
3169:
3168:
3165:
3160:
3159:
3158:
3147:
3141:
3140:
3134:
3133:
3132:
3129:
3124:
3123:
3122:
3112:
3106:
3098:
3095:Zero semigroup
3090:Null semigroup
3086:
3085:
3080:
3078:
3077:
3076:
3043:
3034:
3028:
3027:
3022:
3020:
3019:
3018:
2985:
2976:
2970:
2969:
2964:
2962:
2961:
2960:
2900:
2890:
2881:
2877:
2876:
2870:
2868:
2867:
2866:
2837:
2830:
2829:
2823:
2821:
2820:
2819:
2813:
2796:
2790:
2789:
2783:
2781:
2780:
2779:
2769:
2762:
2752:
2751:
2745:
2743:
2742:
2741:
2731:
2724:
2714:
2713:
2707:
2705:
2704:
2703:
2678:
2672:
2671:
2660:
2658:
2657:
2656:
2646:
2629:
2623:
2622:
2617:
2615:
2614:
2613:
2588:
2567:
2563:
2562:
2557:
2555:
2554:
2553:
2532:
2528:
2527:
2521:
2519:
2518:
2517:
2484:
2480:
2479:
2464:
2462:
2461:
2460:
2444:(depending on
2436:
2424:
2423:
2409:
2407:
2406:
2405:
2389:(depending on
2377:
2369:
2368:
2363:
2361:
2360:
2359:
2339:
2328:
2327:
2321:
2320:
2319:
2314:
2313:
2312:
2299:
2295:
2291:
2288:
2285:
2280:
2276:
2264:
2259:
2252:
2251:
2245:
2243:
2242:
2241:
2235:
2228:
2222:
2221:
2216:
2215:
2214:
2211:
2206:
2205:
2204:
2192:
2186:
2185:
2179:
2177:
2176:
2175:
2155:
2151:
2150:
2145:
2144:
2143:
2140:
2135:
2134:
2133:
2121:
2115:
2114:
2108:
2106:
2105:
2104:
2087:
2083:
2082:
2076:
2074:
2073:
2072:
2048:
2044:
2043:
2038:
2037:
2036:
2033:
2028:
2027:
2026:
2014:
2008:
2007:
2001:
1999:
1998:
1997:
1980:
1974:
1973:
1967:
1965:
1964:
1963:
1946:
1935:
1934:
1928:
1926:
1925:
1924:
1915:
1903:
1897:
1896:
1890:
1888:
1887:
1886:
1875:
1869:
1868:
1862:
1860:
1859:
1858:
1847:
1841:
1840:
1834:
1832:
1831:
1830:
1818:
1810:
1809:
1803:
1801:
1800:
1799:
1765:
1753:
1752:
1746:
1745:
1744:
1741:
1736:
1735:
1734:
1715:
1708:
1707:
1701:
1700:
1699:
1696:
1691:
1690:
1689:
1674:
1662:
1661:
1655:
1653:
1652:
1651:
1640:
1636:
1635:
1629:
1627:
1626:
1625:
1614:
1610:
1609:
1603:
1601:
1600:
1599:
1588:
1584:
1583:
1577:
1575:
1574:
1573:
1562:
1558:
1557:
1551:
1549:
1548:
1547:
1531:
1527:
1526:
1525:p. 69β71
1520:
1518:
1517:
1516:
1503:
1496:
1495:
1489:
1487:
1486:
1485:
1477:
1470:
1469:
1468:p. 69β71
1463:
1461:
1460:
1459:
1446:
1439:
1438:
1432:
1430:
1429:
1428:
1420:
1413:
1412:
1411:p. 69β71
1406:
1404:
1403:
1402:
1389:
1382:
1381:
1375:
1373:
1372:
1371:
1346:
1342:
1341:
1335:
1333:
1332:
1331:
1312:
1290:
1286:
1285:
1279:
1277:
1276:
1275:
1254:
1250:
1249:
1243:
1241:
1240:
1239:
1218:
1214:
1213:
1207:
1205:
1204:
1203:
1184:
1178:
1177:
1171:
1169:
1168:
1167:
1148:
1137:
1130:
1129:
1123:
1122:
1121:
1118:
1113:
1112:
1111:
1100:
1093:
1092:
1091:
1090:
1085:
1077:
1076:
1075:
1072:
1067:
1066:
1065:
1056:
1044:
1038:
1037:
1032:
1031:
1030:
1027:
1022:
1021:
1020:
1008:
1002:
1001:
995:
994:
993:
990:
985:
984:
983:
972:
964:
963:
957:
954:
953:
952:
944:
938:
937:
935:
934:
933:
930:
925:
924:
923:
914:
908:
907:
905:
902:
901:
900:
889:
873:
867:
866:
864:
863:
862:
859:
854:
853:
852:
840:
833:
832:
829:
826:
823:
802:
799:
798:
797:
760:
759:
748:
736:
732:
728:
716:
715:
704:
691:
687:
675:
674:
668:
663:
654:
645:
636:
627:
621:
620:
615:
593:
592:
533:
525:
512:
499:
486:
479:
478:
461:
455:
454:
448:
444:
443:
437:
433:
432:
426:
416:
415:
412:
402:
401:
398:
384:
383:
377:
371:
370:
364:
350:
349:
343:
329:
328:
322:
308:
307:
306:Arbitrary set
304:
298:
297:
288:
282:
281:
275:
269:
268:
262:
256:
255:
249:
243:
242:
239:
233:
232:
229:
216:
213:
200:classification
177:underlying set
149:underlying set
84:
83:
39:
37:
30:
24:
14:
13:
10:
9:
6:
4:
3:
2:
9995:
9984:
9981:
9979:
9976:
9975:
9973:
9961:
9957:
9953:
9949:
9948:
9942:
9940:
9938:
9929:
9928:
9923:
9919:
9917:
9915:
9909:
9903:
9899:
9894:
9892:
9890:
9885:
9881:
9877:
9873:
9869:
9867:
9865:
9861:
9857:
9853:
9849:
9845:
9843:
9841:
9836:
9832:
9828:
9824:
9821:
9819:
9817:
9812:
9811:981-279-000-4
9808:
9804:
9800:
9796:
9794:
9791:
9787:
9783:
9779:
9775:
9771:
9769:
9767:
9763:
9759:
9755:
9751:
9747:
9745:
9743:
9739:
9735:
9731:
9728:
9726:
9724:
9719:
9716:
9712:
9708:
9706:
9704:
9700:
9696:
9692:
9688:
9684:
9682:
9680:
9675:
9672:
9668:
9666:
9664:
9659:
9656:
9652:
9648:
9646:
9644:
9639:
9635:
9631:
9629:
9626:
9622:
9621:0-8218-0272-0
9618:
9614:
9610:
9606:
9604:
9601:
9597:
9593:
9589:
9585:
9581:
9580:G. B. Preston
9577:
9574:
9572:
9570:
9563:
9557:pp. 157, 158
9556:
9553:
9548:
9547:
9546:
9528:
9524:
9520:
9515:
9511:
9507:
9502:
9498:
9489:
9488:
9487:
9470:
9465:
9446:
9445:
9442:pp. 157, 158
9441:
9438:
9433:
9432:
9431:
9415:
9412:
9409:
9401:
9400:
9399:
9383:
9378:
9364:
9363:
9360:pp. 157, 158
9359:
9356:
9351:
9350:
9349:
9333:
9330:
9327:
9319:
9318:
9317:
9301:
9296:
9282:
9281:
9278:pp. 157, 158
9277:
9274:
9269:
9268:
9267:
9251:
9248:
9243:
9239:
9230:
9229:
9228:
9212:
9198:
9197:
9194:pp. 157, 158
9193:
9190:
9185:
9184:
9183:
9165:
9161:
9157:
9154:
9146:
9145:
9144:
9128:
9114:
9113:
9109:
9106:
9101:
9100:
9099:
9094:
9090:
9086:
9085:
9084:
9082:
9079:
9078:
9075:Reference(s)
9074:
9071:
9065:
9064:
9056:
9055:
9048:pp. 151, 158
9047:
9044:
9039:
9038:
9037:
9018:
9014:
9010:
9005:
8995:
8991:
8987:
8982:
8978:
8966:
8963:
8959:
8955:
8952:
8949:
8948:
8947:
8918:
8917:
8914:pp. 150, 158
8913:
8910:
8905:
8904:
8903:
8884:
8880:
8876:
8871:
8867:
8863:
8858:
8854:
8845:
8828:
8824:
8820:
8815:
8811:
8807:
8802:
8798:
8794:
8789:
8785:
8781:
8776:
8772:
8768:
8763:
8759:
8750:
8733:
8729:
8725:
8720:
8716:
8712:
8707:
8703:
8699:
8694:
8690:
8686:
8678:
8675:
8671:
8667:
8664:
8660:
8656:
8653:
8649:
8646:
8645:
8644:
8615:
8614:
8611:pp. 149, 158
8610:
8607:
8602:
8601:
8600:
8581:
8577:
8573:
8568:
8564:
8560:
8552:
8535:
8531:
8527:
8522:
8518:
8514:
8509:
8505:
8501:
8496:
8492:
8488:
8480:
8458:
8449:
8440:
8436:
8433:
8429:
8425:
8422:
8418:
8414:
8411:
8410:
8409:
8360:
8359:
8356:pp. 149, 158
8355:
8352:
8347:
8346:
8345:
8326:
8322:
8318:
8315:
8310:
8306:
8297:
8280:
8276:
8272:
8267:
8263:
8259:
8256:
8251:
8247:
8243:
8238:
8234:
8225:
8203:
8194:
8185:
8181:
8178:
8174:
8170:
8167:
8163:
8159:
8156:
8155:
8154:
8112:
8105:
8104:
8100:
8097:
8092:
8091:
8090:
8085:
8081:
8077:
8073:
8068:
8064:
8062:
8058:
8054:
8050:
8045:
8041:
8025:
8021:
8017:
8012:
8008:
8004:
7996:
7993:
7989:
7986:
7983:
7982:
7981:
7978:
7948:
7947:
7943:
7940:
7935:
7934:
7933:
7917:
7914:
7911:
7889:
7884:
7880:
7871:
7869:
7865:
7861:
7857:
7853:
7850:
7846:
7841:
7837:
7834:, the set of
7833:
7829:
7827:
7823:
7819:
7815:
7810:
7806:
7803:
7786:
7782:
7778:
7773:
7763:
7759:
7753:
7749:
7743:
7739:
7727:
7726:
7725:
7722:
7692:
7691:
7687:
7684:
7679:
7678:
7677:
7672:
7668:
7664:
7661:
7657:
7654:
7653:
7652:
7649:
7617:
7616:
7612:
7609:
7604:
7603:
7602:
7597:
7593:
7589:
7586:
7582:
7579:
7578:
7577:
7574:
7542:
7541:
7537:
7534:
7529:
7528:
7527:
7522:
7519:-trivial and
7518:
7514:
7511:
7507:
7503:
7502:
7501:
7498:
7473:
7472:
7468:
7465:
7460:
7459:
7458:
7439:
7431:
7428:
7422:
7417:
7409:
7406:
7400:
7392:
7389:
7385:
7382:
7381:
7380:
7377:
7352:
7351:
7347:
7344:
7339:
7338:
7337:
7318:
7310:
7307:
7301:
7298:
7293:
7285:
7282:
7271:
7268:
7264:
7261:
7260:
7259:
7256:
7231:
7230:
7226:
7223:
7221:
7216:
7212:
7211:
7210:
7208:
7205:
7204:
7200:
7197:
7192:
7191:
7190:
7185:
7184:
7183:
7181:
7178:
7177:
7174:
7169:
7166:
7165:
7164:
7159:
7155:
7151:
7147:
7143:
7140:There exists
7139:
7136:
7132:
7128:
7124:
7121:There exists
7120:
7119:
7118:
7116:
7113:
7112:
7108:
7105:
7103:
7098:
7097:
7096:
7094:
7091:
7090:
7086:
7083:
7081:
7076:
7072:
7068:
7064:
7060:
7056:
7052:
7048:
7044:
7043:
7042:
7040:
7038:
7034:
7033:
7029:
7026:
7024:
7019:
7015:
7011:
7007:
7003:
6999:
6998:
6997:
6995:
6993:
6989:
6988:
6984:
6981:
6979:
6974:
6970:
6966:
6962:
6958:
6954:
6953:
6952:
6949:
6948:
6945:
6942:
6940:
6935:
6931:
6927:
6923:
6919:
6915:
6911:
6907:
6903:
6902:
6901:
6897:
6894:
6893:
6890:
6887:
6885:
6880:
6876:
6873:
6870:
6866:
6862:
6861:
6860:
6858:
6855:
6854:
6850:
6847:
6845:
6841:
6837:
6833:
6829:
6828:
6827:
6824:
6820:
6817:
6814:Semigroup of
6813:
6812:
6808:
6805:
6803:
6798:
6794:
6791:
6787:
6784:
6780:
6777:Semigroup of
6776:
6775:
6774:
6772:
6769:Semigroup of
6768:
6767:
6763:
6760:
6758:
6753:
6749:
6745:
6741:
6737:
6733:
6729:
6725:
6722:
6718:
6714:
6710:
6706:
6702:
6698:
6694:
6690:
6686:
6682:
6679:
6675:
6672: : Ξ Γ
6671:
6668:
6665:
6661:
6658:
6657:
6656:
6653:
6649:
6648:
6644:
6641:
6639:
6631:
6624:
6617:
6610:
6603:
6596:
6589:
6582:
6576:
6572:
6571:
6570:
6567:
6563:
6560:
6557:
6556:
6552:
6549:
6547:
6542:
6538:
6534:
6530:
6527:
6523:
6519:
6515:
6511:
6507:
6503:
6499:
6495:
6491:
6487:
6484:
6480:
6476:
6472:
6470:
6466:
6462:
6458:
6454:
6450:
6446:
6444:
6440:
6439:
6438:
6436:
6433:
6432:
6428:
6425:
6423:
6418:
6414:
6411:
6407:
6406:
6405:
6402:
6398:
6395:
6392:
6391:
6387:
6384:
6382:
6377:
6373:
6369:
6365:
6361:
6360:
6359:
6356:
6355:
6352:
6349:
6344:
6341:
6340:
6339:
6335:
6331:
6328:Equivalently
6327:
6325:
6321:
6317:
6316:
6315:
6313:
6310:
6309:
6305:
6302:
6300:
6295:
6291:
6287:
6283:
6279:
6276:
6275:
6274:
6269:
6265:
6262:
6259:
6258:
6254:
6251:
6249:
6229:
6226:
6223:
6220:
6217:
6214:
6211:
6208:
6198:
6194:
6191:
6188:
6187:
6186:
6184:
6181:
6180:
6176:
6173:
6168:
6165:
6164:
6163:
6158:
6154:
6150:
6146:
6145:
6144:
6141:
6140:
6136:
6133:
6128:
6125:
6124:
6123:
6119:
6115:
6111:
6107:
6103:
6099:
6096:
6095:
6094:
6091:
6086:
6083:
6082:
6078:
6075:
6073:
6068:
6064:
6060:
6057:is such that
6056:
6052:
6048:
6045:
6042:
6040:
6036:
6035:
6034:
6031:
6030:
6026:
6023:
6021:
6016:
6012:
6008:
6004:
6000:
5996:
5993:
5990:
5988:
5984:
5983:
5982:
5979:
5978:
5974:
5971:
5969:
5964:
5960:
5956:
5952:
5948:
5945:is such that
5944:
5940:
5936:
5933:
5930:
5928:
5924:
5923:
5922:
5919:
5918:
5912:
5909:
5906:
5903:
5900:
5897:
5896:
5895:
5890:
5889:
5888:
5869:
5865:
5861:
5856:
5848:
5845:
5842:
5819:
5816:
5813:
5808:
5804:
5795:
5792:
5788:
5784:
5780:
5776:
5772:
5768:
5764:
5760:
5756:
5750:
5749:
5748:
5721:
5720:
5716:
5713:
5711:
5706:
5702:
5698:
5694:
5689:
5685:
5681:
5677:
5673:
5669:
5665:
5662:
5658:
5654:
5650:
5649:
5648:
5645:
5644:
5640:
5637:
5635:
5631:
5626:
5622:
5619:
5618:
5617:
5612:
5609:
5608:
5604:
5601:
5599:
5594:
5590:
5587:β 0 we have
5586:
5582:
5578:
5574:
5570:
5566:
5562:
5558:
5555:
5551:
5547:
5543:
5539:
5535:
5531:
5528:is such that
5527:
5523:
5519:
5516:
5513:
5511:
5507:
5506:
5505:
5502:
5501:
5497:
5494:
5492:
5487:
5483:
5479:
5475:
5471:
5467:
5463:
5459:
5456:There exists
5455:
5452:
5448:
5444:
5440:
5436:
5432:
5428:
5424:
5420:
5419:
5418:
5415:
5414:
5410:
5407:
5405:
5400:
5396:
5392:
5389:
5387:
5383:
5382:
5381:
5378:
5377:
5373:
5370:
5368:
5364:
5359:
5355:
5352:
5351:
5350:
5347:
5341:
5340:
5336:
5333:
5331:
5327:
5323:
5320:
5317:
5313:
5309:
5306:
5303:
5299:
5296:
5295:
5294:
5291:
5290:
5286:
5283:
5281:
5276:
5272:
5269:
5265:
5261:
5258:
5254:
5251:
5250:
5249:
5246:
5245:
5241:
5238:
5236:
5231:
5227:
5224:
5220:
5216:
5212:
5209:
5208:
5207:
5204:
5203:
5199:
5196:
5194:
5190:
5186:
5181:
5177:
5173:
5168:
5164:
5160:
5156:
5151:
5147:
5145:
5141:
5136:
5132:
5128:
5123:
5119:
5115:
5111:
5106:
5102:
5100:
5096:
5095:
5094:
5091:
5090:
5086:
5083:
5081:
5077:
5073:
5068:
5064:
5060:
5055:
5051:
5047:
5043:
5038:
5034:
5032:
5028:
5027:
5026:
5023:
5022:
5018:
5015:
5013:
5009:
5005:
5000:
4996:
4992:
4987:
4983:
4979:
4975:
4970:
4966:
4964:
4960:
4959:
4958:
4955:
4954:
4950:
4947:
4945:
4940:
4936:
4931:
4927:
4923:
4918:
4914:
4910:
4905:
4901:
4897:
4894:
4890:
4885:
4881:
4877:
4872:
4868:
4864:
4859:
4855:
4851:
4850:
4849:
4846:
4845:
4841:
4838:
4836:
4831:
4827:
4822:
4818:
4814:
4809:
4805:
4801:
4796:
4792:
4788:
4787:
4786:
4783:
4782:
4778:
4775:
4773:
4768:
4764:
4759:
4755:
4751:
4746:
4742:
4738:
4733:
4729:
4725:
4724:
4723:
4720:
4719:
4715:
4712:
4710:
4705:
4701:
4697:
4693:
4689:
4685:
4681:
4677:
4673:
4672:
4671:
4668:
4667:
4663:
4660:
4658:
4653:
4649:
4648:
4647:
4644:
4638:
4637:
4633:
4630:
4628:
4623:
4619:
4616:implies that
4615:
4611:
4607:
4603:
4599:
4595:
4591:
4587:
4584:
4580:
4576:
4573:
4569:
4566:
4563:
4559:
4555:
4551:
4547:
4544:
4542:
4538:
4535:
4534:
4533:
4530:
4529:
4525:
4522:
4520:
4516:
4511:
4507:
4504:
4503:
4502:
4499:
4498:
4494:
4491:
4489:
4485:
4480:
4476:
4473:
4472:
4471:
4468:
4467:
4463:
4460:
4458:
4453:
4448:
4444:
4441:
4440:
4439:
4434:
4431:
4430:
4426:
4423:
4421:
4416:
4411:
4407:
4404:
4403:
4402:
4397:
4394:
4393:
4389:
4386:
4384:
4379:
4376:
4374:
4370:
4367:
4365:
4361:
4358:
4355:
4351:
4347:
4343:
4340:There exists
4339:
4337:
4333:
4330:
4329:
4328:
4325:
4322:
4321:
4317:
4314:
4309:
4306:
4305:
4304:
4299:
4295:
4294:
4293:
4290:
4289:
4285:
4282:
4280:
4275:
4271:
4268:
4267:
4266:
4263:
4262:
4258:
4255:
4253:
4248:
4244:
4240:
4239:
4238:
4235:
4234:
4230:
4227:
4225:
4220:
4216:
4212:
4208:
4204:
4200:
4197:
4196:
4195:
4192:
4191:
4187:
4184:
4182:
4178:
4174:
4170:
4166:
4163:
4160:
4156:
4152:
4148:
4144:
4140:
4139:
4138:
4135:
4132:
4131:
4127:
4124:
4122:
4118:
4114:
4111:
4109:
4105:
4102:
4099:
4095:
4091:
4088:
4086:
4082:
4079:
4078:
4077:
4074:
4073:
4067:
4064:
4061:
4058:
4057:
4056:
4051:
4050:
4049:
4032:
4027:
4023:
4019:
4014:
4010:
4006:
4001:
3997:
3993:
3985:
3981:
3977:
3974:
3970:
3966:
3963:
3961:
3957:
3956:
3955:
3952:
3949:
3948:
3944:
3941:
3939:
3934:
3930:
3927:
3923:
3919:
3916:
3914:
3910:
3907:
3906:
3905:
3902:
3901:
3898:
3895:
3893:
3889:
3885:
3882:
3878:
3874:
3871:
3870:
3869:
3866:
3865:
3862:
3859:
3857:
3853:
3849:
3846:
3845:
3844:
3839:
3838:
3835:
3832:
3830:
3826:
3822:
3819:
3818:
3817:
3812:
3811:
3807:
3804:
3802:
3798:
3794:
3789:
3785:
3784:
3783:
3780:
3779:
3773:
3770:
3767:
3764:
3763:
3762:
3760:
3741:
3737:
3733:
3730:
3725:
3721:
3712:
3708:
3705:
3701:
3698:There exists
3697:
3696:
3695:
3692:
3689:
3688:
3684:
3681:
3679:
3674:
3670:
3667:
3666:
3665:
3662:
3661:
3657:
3654:
3652:
3647:
3643:
3640:
3639:
3638:
3635:
3634:
3630:
3627:
3625:
3620:
3616:
3613:
3610:
3606:
3603:
3602:
3601:
3598:
3597:
3593:
3590:
3588:
3584:
3580:
3576:
3572:
3568:
3565:
3564:
3563:
3560:
3559:
3555:
3552:
3550:
3545:
3541:
3537:
3533:
3529:
3525:
3522:
3518:
3514:
3510:
3506:
3502:
3501:
3500:
3497:
3496:
3492:
3489:
3487:
3482:
3478:
3474:
3470:
3466:
3462:
3461:
3460:
3457:
3456:
3452:
3449:
3447:
3442:
3438:
3434:
3430:
3426:
3422:
3421:
3420:
3417:
3416:
3412:
3409:
3404:
3401:
3400:
3399:
3395:is singleton.
3394:
3391:
3390:
3389:
3386:
3385:
3381:
3378:
3376:
3371:
3370:
3366:
3365:
3364:
3362:
3359:
3358:
3354:
3351:
3349:
3344:
3341:
3340:
3339:
3337:
3334:
3333:
3330:
3327:
3322:
3319:
3318:
3317:
3313:
3309:
3306:
3304:
3300:
3297:
3296:
3294:
3292:
3289:
3288:
3284:
3281:
3276:
3273:
3272:
3271:
3267:
3263:
3260:
3259:
3258:
3256:
3253:
3252:
3248:
3245:
3243:
3238:
3235:
3234:
3233:
3231:
3228:
3227:
3222:
3219:
3218:
3217:
3212:
3209:
3208:
3207:
3203:
3199:
3196:
3194:
3190:
3187:
3186:
3184:
3182:
3179:
3178:
3174:
3171:
3166:
3163:
3162:
3161:
3157:
3153:
3150:
3149:
3148:
3146:
3143:
3142:
3138:
3135:
3130:
3127:
3126:
3125:
3121:
3117:
3114:Equivalently
3113:
3110:
3107:
3105:
3101:
3100:
3099:
3096:
3091:
3088:
3087:
3084:
3081:
3079:
3074:
3070:
3066:
3062:
3058:
3054:
3051:
3046:
3041:
3037:
3036:
3035:
3031:Lpp-semigroup
3030:
3029:
3026:
3023:
3021:
3016:
3012:
3008:
3004:
3000:
2996:
2993:
2988:
2983:
2979:
2978:
2977:
2973:Rpp-semigroup
2972:
2971:
2968:
2965:
2963:
2958:
2954:
2950:
2946:
2942:
2938:
2935:
2931:
2927:
2923:
2919:
2915:
2911:
2908:
2903:
2898:
2893:
2888:
2884:
2883:
2882:
2879:
2878:
2874:
2871:
2869:
2864:
2860:
2856:
2852:
2848:
2844:
2840:
2839:
2838:
2835:
2832:
2831:
2827:
2824:
2822:
2817:
2814:
2811:
2807:
2803:
2800:There exists
2799:
2798:
2797:
2792:
2791:
2787:
2784:
2782:
2777:
2772:
2768:
2765:
2764:
2763:
2760:
2754:
2753:
2749:
2746:
2744:
2739:
2734:
2730:
2727:
2726:
2725:
2722:
2716:
2715:
2711:
2708:
2706:
2701:
2697:
2693:
2689:
2685:
2681:
2680:
2679:
2677:
2674:
2673:
2669:
2664:
2661:
2659:
2654:
2650:
2647:
2644:
2640:
2636:
2633:There exists
2632:
2631:
2630:
2628:
2625:
2624:
2621:
2618:
2616:
2611:
2607:
2603:
2600:
2596:
2592:
2589:
2586:
2582:
2578:
2574:
2571:There exists
2570:
2569:
2568:
2565:
2564:
2561:
2558:
2556:
2551:
2547:
2543:
2539:
2536:There exists
2535:
2534:
2533:
2530:
2529:
2525:
2522:
2520:
2515:
2511:
2507:
2503:
2499:
2495:
2491:
2487:
2486:
2485:
2482:
2481:
2477:
2472:
2468:
2465:
2463:
2459:
2455:
2452:belongs to a
2451:
2447:
2443:
2440:There exists
2439:
2438:
2437:
2434:
2430:
2426:
2425:
2421:
2417:
2413:
2410:
2408:
2403:
2399:
2396:
2392:
2388:
2384:
2381:There exists
2380:
2379:
2378:
2371:
2370:
2367:
2364:
2362:
2357:
2353:
2350:
2346:
2343:There exists
2342:
2341:
2340:
2337:
2333:
2330:
2329:
2325:
2322:
2317:
2316:
2315:
2297:
2293:
2289:
2286:
2283:
2278:
2274:
2265:
2262:
2261:
2260:
2258:
2254:
2253:
2249:
2246:
2244:
2238:
2234:
2231:
2230:
2229:
2227:
2224:
2223:
2220:
2217:
2212:
2209:
2208:
2207:
2203:
2199:
2195:
2194:
2193:
2191:
2188:
2187:
2183:
2180:
2178:
2173:
2169:
2166:
2162:
2159:There exists
2158:
2157:
2156:
2153:
2152:
2149:
2146:
2141:
2138:
2137:
2136:
2132:
2128:
2124:
2123:
2122:
2120:
2117:
2116:
2112:
2109:
2107:
2102:
2098:
2094:
2091:There exists
2090:
2089:
2088:
2085:
2084:
2080:
2077:
2075:
2070:
2066:
2063:
2059:
2055:
2051:
2050:
2049:
2046:
2045:
2042:
2039:
2034:
2031:
2030:
2029:
2025:
2021:
2017:
2016:
2015:
2013:
2010:
2009:
2005:
2002:
2000:
1995:
1991:
1987:
1984:There exists
1983:
1982:
1981:
1979:
1976:
1975:
1971:
1968:
1966:
1961:
1957:
1953:
1950:There exists
1949:
1948:
1947:
1944:
1940:
1937:
1936:
1932:
1929:
1927:
1923:
1919:
1916:
1914:
1910:
1907:
1906:
1904:
1902:
1899:
1898:
1894:
1891:
1889:
1885:
1881:
1878:
1877:
1876:
1874:
1871:
1870:
1866:
1863:
1861:
1857:
1853:
1850:
1849:
1848:
1846:
1843:
1842:
1838:
1835:
1833:
1829:
1825:
1821:
1820:
1819:
1816:
1812:
1811:
1807:
1804:
1802:
1798:
1795:
1791:
1787:
1783:
1780:
1776:
1772:
1768:
1767:
1766:
1763:
1759:
1755:
1754:
1750:
1747:
1742:
1739:
1738:
1737:
1733:
1729:
1726:
1722:
1718:
1717:
1716:
1713:
1710:
1709:
1705:
1702:
1697:
1694:
1693:
1692:
1688:
1685:
1681:
1677:
1676:
1675:
1672:
1668:
1664:
1663:
1659:
1656:
1654:
1650:
1646:
1643:
1642:
1641:
1638:
1637:
1633:
1630:
1628:
1624:
1620:
1617:
1616:
1615:
1612:
1611:
1607:
1604:
1602:
1598:
1594:
1591:
1590:
1589:
1586:
1585:
1581:
1578:
1576:
1572:
1568:
1565:
1564:
1563:
1560:
1559:
1555:
1552:
1550:
1545:
1541:
1537:
1534:
1533:
1532:
1529:
1528:
1524:
1521:
1519:
1515:
1512:
1509:
1506:
1505:
1504:
1501:
1498:
1497:
1493:
1490:
1488:
1483:
1480:
1479:
1478:
1475:
1472:
1471:
1467:
1464:
1462:
1458:
1455:
1452:
1449:
1448:
1447:
1444:
1441:
1440:
1436:
1433:
1431:
1426:
1423:
1422:
1421:
1418:
1415:
1414:
1410:
1407:
1405:
1401:
1398:
1395:
1392:
1391:
1390:
1387:
1384:
1383:
1379:
1376:
1374:
1369:
1365:
1361:
1357:
1353:
1349:
1348:
1347:
1344:
1343:
1339:
1336:
1334:
1329:
1325:
1321:
1317:
1313:
1310:
1306:
1302:
1298:
1294:
1293:
1291:
1288:
1287:
1283:
1280:
1278:
1273:
1269:
1265:
1261:
1257:
1256:
1255:
1252:
1251:
1247:
1244:
1242:
1237:
1233:
1229:
1225:
1221:
1220:
1219:
1216:
1215:
1211:
1208:
1206:
1202:
1198:
1194:
1190:
1187:
1186:
1185:
1183:
1180:
1179:
1175:
1172:
1170:
1165:
1161:
1157:
1153:
1150:There exists
1149:
1147:
1143:
1140:
1139:
1138:
1135:
1132:
1131:
1127:
1124:
1119:
1116:
1115:
1114:
1110:
1106:
1103:
1102:
1101:
1098:
1095:
1094:
1089:
1086:
1083:
1080:
1079:
1078:
1073:
1070:
1069:
1068:
1064:
1060:
1057:
1055:
1051:
1048:
1047:
1045:
1043:
1040:
1039:
1036:
1033:
1028:
1025:
1024:
1023:
1019:
1015:
1011:
1010:
1009:
1007:
1004:
1003:
999:
996:
991:
988:
987:
986:
982:
978:
975:
974:
973:
969:
966:
965:
961:
958:
955:
951:
947:
946:
945:
943:
940:
939:
936:
931:
928:
927:
926:
921:
917:
916:
915:
913:
910:
909:
906:
903:
879:
876:
875:
874:
872:
869:
868:
865:
860:
857:
856:
855:
850:
846:
843:
842:
841:
838:
835:
834:
831:Reference(s)
830:
827:
821:
820:
814:
812:
808:
800:
795:
791:
787:
783:
779:
776:There exists
775:
774:
773:
771:
767:
757:
753:
749:
730:
718:
717:
713:
709:
705:
689:
685:
677:
676:
673:
669:
666:
662:
657:
653:
648:
644:
639:
635:
630:
626:
623:
622:
619:
616:
614:
610:
606:
602:
598:
595:
594:
591:
588:
584:
581:
577:
573:
569:
566:
562:
559:
555:
551:
547:
544:
540:
537:
534:
532:
528:
523:
519:
515:
510:
506:
502:
497:
493:
489:
484:
481:
480:
477:
473:
469:
465:
462:
460:
457:
456:
453:
449:
446:
445:
442:
438:
435:
434:
431:
427:
425:
421:
418:
417:
413:
411:
407:
404:
403:
399:
397:
393:
389:
386:
385:
382:
378:
376:
373:
372:
369:
365:
363:
359:
355:
352:
351:
348:
344:
342:
338:
334:
331:
330:
327:
323:
321:
317:
313:
310:
309:
305:
303:
300:
299:
296:
292:
289:
287:
284:
283:
280:
276:
274:
271:
270:
267:
263:
261:
258:
257:
254:
250:
248:
245:
244:
240:
238:
235:
234:
230:
227:
226:
220:
214:
212:
208:
206:
201:
196:
194:
190:
186:
182:
178:
174:
169:
166:
161:
158:
154:
150:
146:
142:
138:
134:
130:
126:
122:
118:
114:
110:
106:
103:
99:
95:
91:
80:
77:
69:
59:
54:
50:
46:
45:
38:
29:
28:
19:
9951:
9945:
9926:
9897:
9875:
9871:
9847:
9822:
9798:
9773:
9749:
9733:
9717:
9714:
9710:
9686:
9673:
9670:
9654:
9650:
9649:M. Delgado,
9637:
9633:
9608:
9583:
9092:
9088:
9066:Terminology
8961:
8957:
8950:
8673:
8669:
8662:
8661:is equal to
8658:
8651:
8647:
8438:
8431:
8427:
8420:
8416:
8412:
8183:
8176:
8172:
8165:
8161:
8157:
8101:p. 156, 158
8083:
8079:
8075:
8071:
8066:
8060:
8056:
8052:
8048:
8043:
7994:is aperiodic
7991:
7976:
7867:
7863:
7859:
7855:
7848:
7844:
7839:
7835:
7831:
7825:
7821:
7817:
7813:
7808:
7720:
7670:
7666:
7659:
7655:
7647:
7595:
7591:
7584:
7580:
7572:
7520:
7516:
7509:
7505:
7496:
7387:
7383:
7375:
7266:
7262:
7254:
7167:Not infinite
7157:
7153:
7149:
7148:) such that
7145:
7141:
7134:
7130:
7126:
7122:
7074:
7070:
7066:
7062:
7058:
7057:such that (
7054:
7050:
7046:
7036:
7017:
7013:
7012:such that (
7009:
7005:
7001:
6991:
6972:
6968:
6964:
6960:
6956:
6933:
6929:
6925:
6921:
6917:
6913:
6909:
6905:
6878:
6874:
6868:
6864:
6835:
6822:
6818:
6792:
6785:
6783:vector space
6751:
6747:
6743:
6739:
6735:
6731:
6727:
6720:
6716:
6712:
6708:
6704:
6700:
6696:
6692:
6688:
6684:
6677:
6673:
6669:
6663:
6659:
6629:
6622:
6615:
6608:
6601:
6594:
6587:
6580:
6574:
6565:
6561:
6553:p. 101
6540:
6536:
6532:
6525:
6521:
6517:
6513:
6509:
6505:
6504:, such that
6501:
6497:
6493:
6489:
6482:
6478:
6474:
6468:
6464:
6460:
6456:
6452:
6448:
6442:
6416:
6400:
6396:
6375:
6371:
6367:
6363:
6333:
6329:
6323:
6319:
6285:
6267:
6263:
6197:presentation
6192:
6166:Not infinite
6156:
6152:
6148:
6126:Not infinite
6117:
6113:
6109:
6105:
6101:
6097:
6066:
6062:
6058:
6054:
6050:
6043:
6038:
6014:
6010:
6006:
6002:
5998:
5991:
5986:
5962:
5958:
5954:
5950:
5946:
5942:
5938:
5931:
5926:
5913:pp. 151, 158
5790:
5786:
5782:
5778:
5774:
5770:
5766:
5762:
5758:
5751:
5704:
5700:
5696:
5692:
5687:
5683:
5679:
5675:
5671:
5667:
5663:
5660:
5656:
5652:
5629:
5624:
5620:
5610:
5592:
5588:
5584:
5580:
5576:
5572:
5568:
5564:
5560:
5553:
5549:
5545:
5541:
5537:
5533:
5529:
5525:
5521:
5514:
5509:
5485:
5481:
5477:
5473:
5469:
5465:
5461:
5457:
5450:
5446:
5442:
5438:
5434:
5430:
5426:
5422:
5398:
5394:
5390:
5385:
5362:
5357:
5353:
5345:
5325:
5321:
5318:
5315:
5311:
5307:
5304:
5301:
5297:
5274:
5270:
5267:
5263:
5259:
5256:
5252:
5229:
5225:
5222:
5218:
5214:
5210:
5200:p. 178
5188:
5184:
5179:
5175:
5171:
5166:
5162:
5158:
5154:
5149:
5143:
5139:
5134:
5130:
5126:
5121:
5117:
5113:
5109:
5104:
5098:
5087:p. 178
5075:
5071:
5066:
5062:
5058:
5053:
5049:
5045:
5041:
5036:
5030:
5019:p. 178
5007:
5003:
4998:
4994:
4990:
4985:
4981:
4977:
4973:
4968:
4962:
4951:p. 170
4938:
4934:
4929:
4925:
4921:
4916:
4912:
4908:
4903:
4899:
4892:
4888:
4883:
4879:
4875:
4870:
4866:
4862:
4857:
4853:
4842:p. 170
4829:
4825:
4820:
4816:
4812:
4807:
4803:
4799:
4794:
4790:
4779:p. 170
4766:
4762:
4757:
4753:
4749:
4744:
4740:
4736:
4731:
4727:
4703:
4699:
4695:
4691:
4687:
4683:
4679:
4675:
4651:
4634:p. 134
4621:
4617:
4613:
4609:
4605:
4601:
4597:
4593:
4589:
4582:
4578:
4571:
4570:is ideal of
4567:
4561:
4557:
4553:
4549:
4545:
4540:
4536:
4514:
4509:
4505:
4483:
4478:
4474:
4464:p. 362
4451:
4446:
4442:
4432:
4427:p. 362
4414:
4409:
4405:
4395:
4390:p. 100
4377:
4372:
4368:
4363:
4359:
4353:
4349:
4345:
4341:
4335:
4331:
4323:
4318:p. 161
4307:Not infinite
4297:
4286:p. 328
4273:
4269:
4246:
4242:
4241:Equality on
4231:p. 134
4218:
4214:
4210:
4206:
4203:presentation
4198:
4188:p. 245
4176:
4172:
4168:
4164:
4158:
4154:
4150:
4146:
4142:
4133:
4128:p. 111
4116:
4112:
4107:
4103:
4097:
4093:
4089:
4084:
4080:
3983:
3979:
3972:
3968:
3964:
3959:
3951:Nilsemigroup
3945:p. 110
3932:
3925:
3921:
3917:
3912:
3908:
3887:
3883:
3876:
3872:
3851:
3847:
3824:
3820:
3796:
3792:
3787:
3781:Ο-semigroup
3710:
3703:
3699:
3672:
3668:
3645:
3641:
3618:
3614:
3608:
3604:
3582:
3578:
3574:
3570:
3566:
3543:
3539:
3535:
3531:
3527:
3520:
3516:
3512:
3508:
3504:
3480:
3476:
3472:
3468:
3464:
3440:
3436:
3432:
3428:
3424:
3392:
3311:
3307:
3302:
3298:
3265:
3261:
3201:
3197:
3192:
3188:
3155:
3151:
3119:
3115:
3108:
3103:
3072:
3068:
3064:
3060:
3056:
3052:
3049:
3044:
3039:
3014:
3010:
3006:
3002:
2998:
2994:
2991:
2986:
2981:
2956:
2952:
2948:
2944:
2940:
2936:
2933:
2929:
2925:
2921:
2917:
2913:
2909:
2906:
2901:
2896:
2891:
2886:
2885:The classes
2862:
2858:
2854:
2850:
2846:
2842:
2841:There exist
2833:
2828:p. 352
2815:
2809:
2805:
2801:
2788:p. 382
2775:
2770:
2766:
2761:-unipotent)
2758:
2750:p. 382
2737:
2732:
2728:
2723:-unipotent)
2720:
2699:
2695:
2691:
2687:
2683:
2670:p. 226
2652:
2648:
2642:
2638:
2634:
2609:
2605:
2601:
2598:
2594:
2590:
2584:
2580:
2576:
2572:
2549:
2545:
2541:
2537:
2513:
2509:
2505:
2501:
2497:
2493:
2489:
2457:
2449:
2448:) such that
2445:
2441:
2435:for a list)
2401:
2397:
2394:
2393:) such that
2390:
2386:
2382:
2355:
2351:
2348:
2344:
2335:
2331:
2240:is a group.
2236:
2232:
2201:
2197:
2184:p. 121
2171:
2167:
2164:
2160:
2130:
2126:
2113:p. 121
2100:
2096:
2092:
2081:p. 121
2068:
2064:
2061:
2057:
2053:
2052:There exist
2023:
2019:
2012:Regular band
1993:
1989:
1985:
1959:
1955:
1951:
1942:
1921:
1917:
1912:
1908:
1883:
1879:
1855:
1851:
1839:p. 215
1827:
1823:
1808:p. 199
1796:
1793:
1789:
1785:
1781:
1778:
1774:
1770:
1761:
1757:
1751:p. 183
1731:
1727:
1724:
1720:
1706:p. 183
1686:
1683:
1679:
1670:
1666:
1660:p. 119
1648:
1644:
1634:p. 175
1622:
1618:
1608:p. 137
1596:
1592:
1582:p. 137
1570:
1566:
1556:p. 109
1543:
1539:
1535:
1513:
1510:
1507:
1499:
1481:
1473:
1456:
1453:
1450:
1442:
1424:
1416:
1399:
1396:
1393:
1385:
1367:
1363:
1359:
1355:
1351:
1327:
1323:
1319:
1315:
1314:There exist
1308:
1304:
1300:
1296:
1295:There exist
1271:
1267:
1263:
1259:
1258:There exist
1235:
1231:
1227:
1223:
1222:There exist
1200:
1196:
1192:
1188:
1176:p. 131
1163:
1159:
1155:
1151:
1145:
1141:
1108:
1104:
1062:
1058:
1053:
1049:
1017:
1013:
980:
976:
949:
919:
877:
858:Not infinite
844:
822:Terminology
804:
793:
789:
785:
781:
777:
769:
765:
763:
755:
751:
707:
671:
664:
660:
655:
651:
646:
642:
637:
633:
628:
624:
612:
608:
604:
600:
596:
589:
586:
582:
579:
575:
571:
567:
564:
560:
557:
553:
549:
545:
542:
538:
535:
530:
526:
521:
517:
513:
508:
504:
500:
495:
491:
487:
482:
475:
471:
467:
463:
458:
451:
440:
429:
423:
419:
409:
405:
395:
391:
387:
380:
374:
367:
361:
357:
353:
346:
340:
336:
332:
325:
319:
315:
311:
301:
294:
293:elements of
285:
278:
272:
265:
259:
252:
246:
236:
218:
209:
197:
162:
140:
136:
132:
128:
108:
98:nonempty set
87:
72:
66:October 2012
63:
56:Please help
52:
41:
9730:J. M. Howie
8953:is a group,
6840:composition
6830:Set of all
6750:, Ξ ;
6645:p. 18
6429:p. 29
6388:p. 97
6195:admits the
6177:p. 20
6137:p. 19
6079:p. 67
6027:p. 67
5975:p. 67
5777:such that
5641:p. 49
5605:p. 76
5498:p. 76
5437:such that
5411:p. 76
5393:- {0} is a
5374:p. 49
5337:p. 35
5287:p. 35
5242:p. 35
4716:p. 11
4526:p. 57
4495:p. 57
4326:-semigroup
4259:p. 88
4221:are finite.
4213:) in which
3880:is a group.
3867:Orthogroup
3685:p. 34
3658:p. 34
3631:p. 34
3413:p. 21
3336:Right group
2875:p. 98
2712:p. 28
2526:p. 26
2473:p. 110
2422:p. 49
2347:such that
2326:p. 65
2250:p. 75
2006:p. 26
1972:p. 98
1815:exponential
1760:semigroup (
1712:Exponential
1669:semigroup (
1542:) for some
1380:p. 77
1340:p. 59
1322:such that (
1303:such that (
1284:p. 59
1266:such that (
1248:p. 59
1230:such that (
1212:p. 26
1134:Archimedean
1097:Commutative
1042:Semilattice
758:is finite.
754:, assuming
153:cardinality
151:has finite
125:commutative
102:associative
90:mathematics
60:if you can.
9972:Categories
9687:Semigroups
9564:References
7862:such that
7838:such that
7039:-semigroup
6994:-semigroup
6983:C&P II
6963:such that
6916:such that
6707:, ΞΌ ) = (
6691:Γ Ξ by (
6654:semigroup
6410:one-to-one
6306:p. 2
6129:Not finite
5907:p. 16
5397:-class of
4664:p. 2
4348:such that
4300:is finite.
4145:such that
4062:p. 99
3768:p. 29
3556:p. 4
3493:p. 4
3453:p. 9
3285:p. 4
3230:Left group
3175:p. 4
3139:p. 4
3038:The class
2980:The class
2849:such that
2804:such that
2686:such that
2665:p. 57
2637:such that
2579:such that
2544:such that
2478:p. 4
2255:(inverse)
2163:such that
2095:such that
2060:such that
1988:such that
1954:such that
1933:p. 3
1895:p. 3
1867:p. 3
1817:semigroup
1714:semigroup
1158:such that
1128:p. 3
1099:semigroup
1084:p. 24
1000:p. 4
962:p. 3
849:finite set
839:semigroup
796:are equal.
223:Notations
185:structures
121:properties
117:semigroups
9691:CRC Press
9529:ω
9516:ω
9508:≤
9503:ω
9413:≤
9384:−
9331:≤
9249:≤
9244:ω
9213:−
9166:ω
9158:≤
9019:ω
9006:ω
8996:ω
8983:ω
8885:ω
8872:ω
8859:ω
8821:…
8795:…
8769:…
8726:…
8700:…
8582:ω
8569:ω
8528:…
8502:…
8327:ω
8311:ω
8273:…
8244:…
8113:ℓ
8026:ω
8013:ω
7915:×
7787:ω
7774:ω
7764:ω
7754:ω
7744:ω
7523:-trivial.
7440:ω
7418:ω
7319:ω
7294:ω
7215:recognize
6881:is finite
6535:β 0 and
6351:Fennemore
6233:⟩
6218:∣
6206:⟨
5901:p. 5
5870:ω
5857:ω
5809:ω
5273:for some
5228:for some
4369:xa = ya
4028:ω
4015:ω
4002:ω
3924:for some
3742:ω
3726:ω
3329:Fennemore
3221:Fennemore
2604:for some
2298:ω
2279:ω
2219:Fennemore
2148:Fennemore
2041:Fennemore
1088:Fennemore
1035:Fennemore
888:∅
690:ω
228:Notation
215:Notations
165:algebraic
94:semigroup
9754:Springer
9732:(1995),
9676:, 23β38
9582:(1964).
9072:Variety
8078:implies
8055:implies
7866:but not
7820:implies
7093:Semiband
6734:, Ξ )/(
6699:, Ξ» ) (
6662:a group
6477:β 0 and
6342:Infinite
6282:mappings
5480:we have
4690:for all
4581:is 0 of
4577:Zero of
4360:ax = ay
3534:for all
3511:for all
3471:for all
3431:for all
3402:Infinite
3320:Infinite
3274:Infinite
3210:Infinite
3164:Infinite
3128:Infinite
3048:, where
2990:, where
2905:, where
2454:subgroup
2429:epigroup
2210:Infinite
2139:Infinite
2032:Infinite
1918:ba = ca
1909:ab = ac
1880:ab = ac
1852:ba = ca
1826:for all
1740:Infinite
1730:for all
1695:Infinite
1366:for all
1117:Infinite
1071:Infinite
1026:Infinite
989:Infinite
929:Infinite
231:Meaning
193:topology
42:require
9837:, 1986
9627:
9602:
7868:ef J e
7688:p. 158
7613:p. 158
7538:p. 158
7469:p. 158
7348:p. 158
7201:p. 130
6849:C&P
6807:C&P
6788:over a
6762:C&P
6628:, ...,
6614:, ...,
6600:, ...,
6586:, ...,
6551:C&P
6455:β 0 or
6427:C&P
6386:C&P
6304:C&P
6280:of all
6253:C&P
6175:C&P
6135:C&P
6077:C&P
6025:C&P
5973:C&P
5899:C&P
5715:C&P
5639:C&P
5603:C&P
5548:= 0 or
5496:C&P
5409:C&P
5372:C&P
4714:C&P
4662:C&P
3683:C&P
3656:C&P
3629:C&P
3592:C&P
3554:C&P
3491:C&P
3451:C&P
3411:C&P
3353:C&P
3283:C&P
3247:C&P
3173:C&P
3137:C&P
2873:C&P
2710:C&P
2524:C&P
2338:fixed)
2324:Petrich
2182:C&P
2111:C&P
2079:C&P
2004:C&P
1970:C&P
1931:C&P
1893:C&P
1865:C&P
1813:Weakly
1764:fixed)
1673:fixed)
1210:C&P
1174:C&P
1126:C&P
1082:C&P
998:C&P
807:variety
466:if 1 β
291:Regular
175:of the
173:subsets
163:In the
44:cleanup
9904:
9882:
9809:
9784:
9760:
9697:
9651:et al.
9619:
9594:
9549:Finite
9434:Finite
9352:Finite
9270:Finite
9186:Finite
9110:p. 14
9102:Finite
9040:Finite
8906:Finite
8603:Finite
8348:Finite
8093:Finite
7936:Finite
7826:v L av
7822:v R va
7680:Finite
7605:Finite
7530:Finite
7495:: the
7461:Finite
7374:: the
7340:Finite
7253:: the
7227:p. 14
7170:Finite
7109:p.230
7087:p.102
7061:β)β =
7030:p.102
7016:β)β =
6838:under
6795:under
6723:, ΞΌ ).
6715:P( Ξ»,
6680:a map.
6652:matrix
6607:) = (
6345:Finite
6169:Finite
5891:Finite
4556:where
4310:Finite
4201:has a
4068:p. 148
4052:Finite
3774:p. 158
3405:Finite
3382:p. 87
3323:Finite
3277:Finite
3213:Finite
3167:Finite
3131:Finite
2318:Finite
2213:Finite
2142:Finite
2035:Finite
1743:Finite
1698:Finite
1120:Finite
1074:Finite
1029:Finite
992:Finite
942:Monoid
932:Finite
861:Finite
837:Finite
168:theory
145:finite
9931:(PDF)
9835:India
7864:e J f
7115:Group
7053:β in
7008:β in
6985:Ch.8
6928:)* =
6924:and (
6920:** =
6912:* in
6851:p.13
6809:p.57
6790:field
6781:of a
6764:p.88
6650:Rees
6189:1 β S
6065:then
6013:then
5961:then
5785:and
5544:then
5472:and
5445:and
4915:then
4869:then
4806:then
4743:then
4698:then
4373:x = y
4364:x = y
4100:where
3538:then
3515:then
3475:then
3435:then
2932:and
2591:e D f
2508:then
2020:abaca
1922:b = c
1913:b = c
1884:b = c
1856:b = c
1788:) = (
1358:then
922:is 1.
847:is a
205:group
189:order
187:like
113:class
111:is a
96:is a
9902:ISBN
9880:ISBN
9807:ISBN
9782:ISBN
9758:ISBN
9695:ISBN
9617:ISBN
9592:ISBN
7858:and
7824:and
7107:Howi
7085:Howi
7065:and
7028:Howi
6959:of
6944:Howi
6889:Delg
6863:0 β
6643:Gril
6593:) (
6543:β 0.
6541:eSf
6441:0 β
6100:= {
6069:= 0.
6037:0 β
6017:= 0.
5985:0 β
5965:= 0.
5953:and
5925:0 β
5905:Higg
5832:and
5682:) β
5674:) =
5659:) =
5651:Let
5583:and
5536:and
5508:0 β
5384:0 β
5335:Nagy
5285:Nagy
5240:Nagy
5198:Gril
5148:0 β
5103:0 β
5085:Gril
5035:0 β
5017:Gril
4967:0 β
4949:Gril
4840:Gril
4777:Gril
4682:and
4632:Gril
4600:and
4588:For
4524:Gril
4493:Gril
4462:Gril
4425:Gril
4388:Gril
4316:Gril
4284:Gril
4257:Gril
4229:Gril
4217:and
4186:Gril
4153:and
4126:Gril
4060:Gril
3982:and
3958:0 β
3943:Gril
3897:Shum
3861:Shum
3834:Shum
3806:Gril
3380:Nagy
3102:0 β
3083:Shum
3025:Shum
2967:Chen
2895:and
2859:byac
2857:and
2851:baxc
2845:and
2826:Gril
2786:Gril
2748:Gril
2694:and
2668:Howi
2663:Gril
2496:and
2476:Higg
2471:Gril
2467:Kela
2433:Kela
2420:Higg
2416:Shum
2412:Edwa
2385:and
2366:Hari
2248:Gril
2056:and
2024:abca
1837:Nagy
1806:Nagy
1777:) =
1749:Nagy
1723:) =
1704:Nagy
1682:) =
1658:Nagy
1649:xbay
1645:xaby
1632:Nagy
1606:Nagy
1580:Nagy
1554:Nagy
1523:Nagy
1492:Nagy
1466:Nagy
1435:Nagy
1409:Nagy
1378:Nagy
1338:Nagy
1326:) =
1318:and
1307:) =
1299:and
1282:Nagy
1270:) =
1262:and
1246:Nagy
1234:) =
1226:and
1154:and
1018:acba
1014:abca
968:Band
960:Gril
948:1 β
792:and
784:and
570:and
181:sets
139:and
107:. A
92:, a
9956:doi
9856:doi
9805:,
9780:.
9693:.
9615:.
9590:.
9555:Pin
9440:Pin
9358:Pin
9276:Pin
9192:Pin
9108:Pin
9046:Pin
8951:eSe
8912:Pin
8670:eaf
8648:eSe
8609:Pin
8354:Pin
8099:Pin
8080:efe
8057:eae
7942:Pin
7686:Pin
7667:aba
7611:Pin
7592:aba
7536:Pin
7467:Pin
7346:Pin
7225:Pin
7199:Pin
6834:on
6488:If
6485:β 0
6483:abc
6415:of
6330:abc
6320:aba
6292:as
6284:of
6278:Set
6116:in
6108:,
6049:If
6046:β 0
5997:If
5994:β 0
5937:If
5934:β 0
5911:Pin
5793:.),
5575:,
5563:in
5520:If
5517:β 0
5460:in
5178:or
5133:or
5097:0β
5065:or
5029:0β
4997:or
4961:0β
4928:or
4898:If
4882:or
4852:If
4819:or
4789:If
4756:or
4726:If
4694:in
4674:If
4604:in
4596:in
4539:=
4380:= Γ
4352:=
4155:xax
4147:axa
4083:=
4066:Pin
3986:,
3772:Pin
3766:KKM
3675:β Γ
3648:β Γ
3621:β Γ
3611:β Γ
3526:If
3503:If
3463:If
3423:If
3111:= 0
3063:=
3059:if
3005:=
3001:if
2947:=
2943:if
2920:=
2916:if
2806:axa
2696:xax
2688:axa
2639:axa
2620:Tvm
2608:in
2581:aua
2575:in
2560:Tvm
2546:aua
2540:in
2488:If
2456:of
2198:aba
2127:aba
1990:axa
1822:WE-
1756:WE-
1623:bxa
1619:axb
1597:bax
1593:abx
1571:xba
1567:xab
1538:= (
1364:bxa
1360:axb
1350:If
1162:=
1109:ba
1063:ba
1061:=
1059:ab
956:No
904:No
794:xba
790:xab
770:xba
766:xab
191:or
115:of
88:In
9974::
9950:,
9886:.
9876:29
9850:,
9833:,
9829:,
9825:,
9776:.
9756:.
9752:.
9736:,
9718:10
9689:.
9674:28
9657:,
9653:,
9638:11
9578:,
9091:β€
8674:ef
8672:=
8650:=
8419:=
8417:Se
8415::
8164:=
8162:eS
8160::
8082:=
8059:=
7671:ba
7669:=
7596:ab
7594:=
7156:=
7154:xa
7152:=
7150:ax
7133:=
7131:ha
7129:=
7127:ah
7073:=
7067:aa
7049:β
7004:β
6971:(
6967:β
6936:*.
6926:ab
6908:β
6877:-
6867:β
6754:).
6746:;
6742:(
6730:,
6726:(
6719:)
6711:,
6703:,
6695:,
6687:Γ
6676:β
6621:,
6579:(
6531:(
6524:=
6522:za
6520:,
6516:=
6514:ay
6512:,
6508:=
6506:xa
6500:,
6496:,
6479:bc
6475:ab
6473:(
6467:=
6461:cb
6459:=
6457:ca
6453:bc
6451:=
6449:ac
6447:(
6376:by
6374:,
6372:bx
6370:,
6368:ay
6366:,
6364:ax
6334:ac
6332:=
6322:=
6155:,
6151:,
6147:{
6104:,
6092:)
6061:β
6059:AS
6053:β
6009:β
6007:SA
6001:β
5957:β
5955:SA
5949:β
5947:AS
5941:β
5789:β
5787:AS
5781:β
5779:SA
5773:β
5769:,
5765:β
5757:=
5699:)/
5666:,
5664:aS
5628:=
5591:=
5579:=
5577:fh
5571:=
5569:hf
5552:=
5540:β
5538:SA
5532:β
5530:AS
5524:β
5484:=
5478:f
5476:=
5474:fh
5468:=
5466:hf
5449:β
5447:AS
5441:β
5439:SA
5433:β
5429:,
5425:β
5361:=
5314:β
5300:β
5266:β
5255:β
5221:β
5215:bS
5213:β
5161:,
5116:,
5048:,
4980:,
4902:,
4856:,
4793:,
4730:,
4702:=
4688:zy
4686:=
4684:zx
4680:yz
4678:=
4676:xz
4645:)
4620:=
4614:cy
4612:=
4610:cx
4608:,
4592:,
4552:βͺ
4548:=
4541:ba
4537:ab
4513:=
4482:=
4354:xb
4336:ba
4334:=
4332:ab
4209:;
4205:(
4175:β
4167:=
4165:ea
4157:=
4149:=
4096:βͺ
4085:ba
4081:ab
3913:ba
3911:=
3909:ab
3852:aS
3850:β
3848:Sa
3825:Sa
3823:β
3821:aS
3713:,
3673:bS
3671:β©
3669:aS
3646:Sb
3644:β©
3642:Sa
3619:bS
3617:β©
3615:aS
3609:Sb
3607:β©
3605:Sa
3581:=
3573:=
3569:=
3567:ab
3542:=
3532:bx
3530:=
3528:ax
3519:=
3509:xb
3507:=
3505:xa
3479:=
3469:bx
3467:=
3465:ax
3439:=
3429:xb
3427:=
3425:xa
3310:=
3308:aa
3301:=
3299:ab
3264:=
3262:ab
3200:=
3198:aa
3191:=
3189:ab
3154:=
3152:ab
3120:cd
3118:=
3116:ab
3109:ab
3097:)
3073:db
3071:=
3069:cb
3067:β
3065:da
3061:ca
3055:*
3015:bd
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