2663:
2395:
4680:
337:
2237:
1838:
464:
1907:
3546:
3226:
938:
4188:
2796:
1963:
2326:
4110:
2718:
2131:
1371:
1281:
2956:
is the common length of any composition series of the module; the length is infinite if there is no composition series. Over a field, the length is more commonly known as the
4468:
1493:
3486:
3166:
1669:
3603:
3283:
4802:
4429:
3654:
3334:
2085:
4058:
3372:
2658:
200:) is a module in which all systems of equations can be decided by finitary means. Alternatively, those modules which leave pure-exact sequence exact after applying Hom.
4026:
3974:
3919:
3691:
2626:
2574:
2519:
2321:
1208:
1159:
390:
3454:
3134:
1398:
4359:
4227:
of a module is the minimal length of (if any) a finite projective resolution of the module; the dimension is infinite if there is no finite projective resolution.
4769:
4749:
4729:
4709:
4379:
4328:
4308:
4288:
4210:
4136:
3994:
3942:
3887:
3863:
3843:
3422:
3402:
3099:
3076:
2744:
2594:
2542:
2487:
2463:
2443:
2415:
2153:
2045:
1862:
1787:
1707:
1628:
1608:
1553:
1533:
1513:
1437:
1248:
1228:
1179:
1133:
579:
559:
361:
250:
230:
2904:
3749:
is a module such that every submodule is finitely generated. Equivalently, every increasing chain of submodules becomes stationary after finitely many steps.
2280:
is a non-zero module that cannot be written as a direct sum of two non-zero submodules. Every simple module is indecomposable (but not conversely).
2937:
says that (1) a finite-length module admits an indecomposable decomposition and (2) any two indecomposable decompositions of it are equivalent.
5071:
5019:
4989:
255:
3813:
643:
over a ring is the category where the objects are all the (say) left modules over the given ring and the morphisms module homomorphisms.
5097:
5066:, The Wadsworth & Brooks/Cole Mathematics Series, Pacific Grove, CA: Wadsworth & Brooks/Cole Advanced Books & Software,
5052:
4966:
2160:
40:
3790:
3034:
1751:
of the module if the submodule generated by the set (i.e., the smallest subset containing the set) is the entire module itself.
1999:
1792:
395:
2877:
1008:
is the set of all module homomorphisms with addition as addition of functions and multiplication composition of functions.
1867:
589:
193:
3495:
3175:
977:
4497:
is the intersection of the maximal submodules. For
Artinian modules, the smallest submodule with semisimple quotient.
2957:
879:
is a module that is the direct sum of the underlying abelian group together with component-wise scalar multiplication.
4259:
1993:
2390:{\displaystyle \operatorname {length} (\operatorname {coker} (f))-\operatorname {length} (\operatorname {ker} (f))}
1748:
1689:
is a module that has a basis, or equivalently, one that is isomorphic to a direct sum of copies of the scalar ring
898:
864:
781:
28:
2934:
2006:
688:
4831:
1912:
1635:
1440:
1404:
1296:
824:
703:
209:
581:
such that every element in the module can be expressed as a finite sum of elements in the basis in a unique way.
4935:
3044:
2986:
1408:
1320:
749:
4069:
2677:
2289:
2810:(also called injective hull) is a maximal essential extension, or a minimal embedding in an injective module.
844:
4505:
4144:
2894:
2825:
2752:
2265:
34:
5102:
4537:
3734:
3002:
2090:
1330:
4816:
over a commutative ring is the set of prime ideals at which the localizations of the module are nonzero.
2814:
2277:
2017:
1717:
1253:
876:
197:
478:
is a module in which every decreasing chain of submodules becomes stationary after finitely many steps.
673:
4527:
4434:
4224:
1446:
1078:
513:
20:
3459:
3139:
1641:
727:
4862:
4813:
4623:
4571:
4494:
3716:
3700:
2969:
2134:
1036:
677:
640:
340:
4683:
says that a finitely generated modules over PIDs are finite direct sums of primary cyclic modules.
3555:
3235:
4872:
4842:
4778:
4669:
4384:
3818:
3609:
3289:
3079:
2953:
2807:
2050:
1308:
1021:
987:
760:
4592:
4031:
3340:
2631:
1570:
3699:
3. All the modules together with all the module homomorphisms between them form the
5067:
5048:
5015:
4985:
4962:
4658:
4635:
3999:
3947:
3892:
3866:
3801:
3746:
3660:
2836:
2599:
2547:
2492:
2294:
1981:
1184:
1016:
1005:
962:
is a module over a ring of functions on algebraic curve with coefficients from a finite field.
770:
738:
628:
4602:
4581:
4516:
4231:
2466:
1759:
1138:
948:
651:
624:
487:
369:
5081:
5029:
4999:
3427:
3107:
1376:
5077:
5025:
5011:
4995:
4984:, Monographs and Textbooks in Pure and Applied Mathematics, vol. 147, Marcel Dekker,
4471:
3773:
3712:
2976:
1113:
959:
699:
531:
475:
4336:
1535:
is a finite linear combination of those elements with coefficients from the scalar ring
5044:
4978:
4958:
4951:
4908:
4890:
4754:
4734:
4714:
4694:
4364:
4331:
4313:
4293:
4273:
4242:
4195:
4121:
3979:
3927:
3872:
3848:
3828:
3779:
3407:
3387:
3084:
3061:
2923:
2729:
2579:
2527:
2472:
2448:
2428:
2400:
2138:
2030:
1847:
1772:
1692:
1613:
1593:
1538:
1518:
1498:
1422:
1233:
1213:
1164:
1118:
1058:
564:
544:
516:
says that two decompositions into modules with local endomorphism rings are equivalent.
346:
235:
215:
5091:
4647:
4113:
3102:
3024:
2848:
2721:
1841:
1736:
1672:
1564:
1292:
793:
661:
16:
3382:
998:
502:
498:
2817:
is an injective module such that every module has a nonzero homomorphism into it.
4928:
4893:
is a module in which every two non-zero submodules have a non-zero intersection.
4852:
4612:
3812:
3056:
2860:
2247:
1686:
1631:
1068:
784:
is a module that admits a generating set whose cardinality is at most countable.
2662:
5036:
4681:
structure theorem for finitely generated modules over a principal ideal domain
3922:
1580:
4772:
2522:
2915:
The kernel of a module homomorphism is the pre-image of the zero element.
812:
715:
607:
702:
is a finitely generated module whose finitely generated submodules are
4584:
says that the endomorphism ring of a simple module is a division ring.
4519:
is a module that is isomorphic via the natural map to its second dual.
4262:
states that a finite projective module over a polynomial ring is free.
332:{\displaystyle {\textrm {Ann}}(M):=\{r\in R~|~rm=0\,\forall m\in M\}}
3811:
2661:
3168:(called scalar multipliction) satisfies the following condition:
718:
of a module homomorphism is the codomain quotiented by the image.
2839:
over a commutative ring is a rank-one finite projective module.
4650:
is a nonzero module whose only submodules are zero and itself.
2232:{\displaystyle r\phi (m)=\phi (rm)\,\forall r\in R,m\in M_{1}}
23:
are studied. This is a glossary of some terms of the subject.
47:
3816:
The characteristic property of projective modules is called
2009:
tells when a
Hilbert–Poincaré series is a rational function.
5010:, Graduate Texts in Mathematics No. 189, Berlin, New York:
827:
is a way to express a module as a direct sum of submodules.
4938:
is a module homomorphism that maps every element to zero.
599:"big" usually means "not-necessarily finitely generated".
2907:
says that a projective module over a local ring is free.
847:
of a finite free module over a commutative ring is the
1311:
is a module that admits a (finite) composition series.
4781:
4757:
4737:
4717:
4697:
4437:
4387:
4367:
4339:
4316:
4296:
4276:
4198:
4147:
4124:
4072:
4034:
4002:
3982:
3950:
3930:
3895:
3875:
3851:
3831:
3663:
3612:
3558:
3498:
3462:
3430:
3410:
3390:
3343:
3292:
3238:
3178:
3142:
3110:
3087:
3064:
2863:
between modules is an invertible module homomorphism.
2755:
2732:
2680:
2634:
2602:
2582:
2550:
2530:
2495:
2475:
2451:
2431:
2403:
2329:
2297:
2163:
2141:
2093:
2053:
2033:
1915:
1870:
1850:
1833:{\displaystyle A=\bigoplus _{n\in \mathbb {N} }A_{n}}
1795:
1775:
1695:
1644:
1616:
1596:
1541:
1521:
1501:
1449:
1425:
1379:
1333:
1256:
1236:
1216:
1187:
1167:
1141:
1121:
901:
567:
547:
459:{\displaystyle {\textrm {Ann}}(m):=\{r\in R~|~rm=0\}}
398:
372:
349:
258:
238:
218:
867:
or dg-module is a graded module with a differential.
1984:
of a module homomorphism is another term for index.
1902:{\displaystyle \bigoplus _{i\in \mathbb {N} }M_{i}}
4977:
4950:
4796:
4763:
4743:
4723:
4703:
4462:
4423:
4373:
4353:
4322:
4302:
4282:
4204:
4182:
4130:
4104:
4052:
4020:
3988:
3968:
3936:
3913:
3881:
3857:
3837:
3685:
3648:
3597:
3540:
3480:
3448:
3416:
3396:
3366:
3328:
3277:
3220:
3160:
3128:
3093:
3070:
2790:
2738:
2712:
2652:
2620:
2588:
2568:
2536:
2513:
2481:
2457:
2437:
2409:
2389:
2315:
2231:
2147:
2125:
2079:
2039:
1957:
1901:
1856:
1832:
1781:
1739:is a module over the group ring of a Galois group.
1701:
1663:
1622:
1602:
1547:
1527:
1507:
1487:
1431:
1392:
1365:
1275:
1242:
1222:
1202:
1173:
1153:
1127:
932:
815:is a module over a ring of differential operators.
573:
553:
458:
384:
355:
331:
244:
224:
4234:is a minimal surjection from a projective module.
3541:{\displaystyle \forall r,s\in R,\forall m,n\in M}
3221:{\displaystyle \forall r,s\in R,\forall m,n\in M}
2968:1. A linear map is another term for a
2666:The module Q is injective if the diagram commutes
1001:is a module homomorphism from a module to itself.
3737:is an endomorphism, some power of which is zero.
4217:In particular, every free module is projective.
1677:In particular, every projective module is flat.
1046:is a submodule that every nonzero submodule of
3793:is a cyclic indecomposable projective module.
933:{\displaystyle \operatorname {Hom} _{R}(M,R)}
8:
4931:is a module consisting of only zero element.
453:
418:
366:2. The annihilator of an element
326:
278:
1958:{\displaystyle A_{i}M_{j}\subseteq M_{i+j}}
4953:Introductory Lectures on Rings and Modules
2905:Kaplansky's theorem on a projective module
2268:is an endomorphism whose square is itself.
4780:
4756:
4736:
4716:
4696:
4450:
4436:
4386:
4366:
4343:
4338:
4315:
4295:
4275:
4197:
4146:
4123:
4081:
4075:
4074:
4071:
4063:The following conditions are equivalent:
4033:
4001:
3981:
3949:
3929:
3894:
3874:
3850:
3830:
3671:
3662:
3611:
3557:
3497:
3461:
3429:
3409:
3389:
3354:
3348:
3342:
3291:
3237:
3177:
3141:
3109:
3086:
3063:
2754:
2731:
2689:
2683:
2682:
2679:
2671:The following conditions are equivalent:
2633:
2601:
2581:
2549:
2529:
2494:
2474:
2450:
2430:
2402:
2328:
2296:
2223:
2197:
2162:
2140:
2117:
2104:
2092:
2071:
2058:
2052:
2032:
1943:
1930:
1920:
1914:
1893:
1883:
1882:
1875:
1869:
1849:
1824:
1814:
1813:
1806:
1794:
1774:
1694:
1652:
1643:
1615:
1595:
1540:
1520:
1500:
1479:
1454:
1448:
1424:
1384:
1378:
1351:
1338:
1332:
1258:
1257:
1255:
1235:
1215:
1186:
1166:
1140:
1120:
906:
900:
566:
546:
433:
400:
399:
397:
371:
348:
313:
293:
260:
259:
257:
237:
217:
4105:{\displaystyle {\textrm {Hom}}_{R}(P,-)}
2713:{\displaystyle {\textrm {Hom}}_{R}(-,I)}
1135:is one where the action of each nonzero
4976:Golan, Jonathan S.; Head, Tom (1991),
4183:{\displaystyle 0\to L\to L'\to P\to 0}
2791:{\displaystyle 0\to I\to L\to L'\to 0}
1443:if there exist finitely many elements
851:-th exterior power of the module when
19:is the branch of mathematics in which
7:
4920:
4901:
4882:
4824:
4626:is the largest semisimple submodule.
4564:
4486:
4251:
4212:is a direct summand of free modules.
3765:
3726:
3017:
2945:
2887:
2870:
2257:
2126:{\displaystyle \phi :M_{1}\to M_{2}}
1973:
1728:
1400:are finitely generated free modules.
1105:
970:
804:
617:
524:
186:
3488:satisfies the following condition:
1366:{\displaystyle F_{1}\to F_{0}\to M}
4980:Modules and the structure of rings
4638:is a direct sum of simple modules.
3719:with an action of a ring spectrum.
3520:
3499:
3200:
3179:
2397:, when the cokernel and kernel of
2198:
1276:{\displaystyle {\textrm {Ann}}(M)}
796:if it is generated by one element.
314:
14:
1864:can be expressed as a direct sum
1747:A subset of a module is called a
627:(the term "canonical" comes from
41:Glossary of representation theory
761:Jordan Hölder composition series
4463:{\displaystyle r\in R,\,m\in M}
3791:principal indecomposable module
1488:{\displaystyle x_{1},...,x_{n}}
172:
4540:uses a ring homomorphism from
4403:
4391:
4174:
4168:
4157:
4151:
4099:
4087:
4012:
3960:
3905:
3643:
3634:
3622:
3613:
3571:
3559:
3481:{\displaystyle M\times R\to M}
3472:
3443:
3431:
3320:
3311:
3305:
3296:
3254:
3242:
3161:{\displaystyle R\times M\to M}
3152:
3123:
3111:
2782:
2771:
2765:
2759:
2707:
2695:
2612:
2560:
2505:
2384:
2381:
2375:
2366:
2354:
2351:
2345:
2336:
2307:
2194:
2185:
2176:
2170:
2110:
1664:{\displaystyle -\otimes _{R}F}
1357:
1344:
1270:
1264:
1081:uses a ring homomorphism from
927:
915:
434:
412:
406:
294:
272:
266:
1:
5008:Lectures on modules and rings
167:
3598:{\displaystyle (m+n)r=mr+nr}
3278:{\displaystyle r(m+n)=rm+rn}
3035:Mitchell's embedding theorem
3030:Mitchell's embedding theorem
887:The dual module of a module
505:that is also an isomorphism.
194:algebraically compact module
5062:Passman, Donald S. (1991),
4797:{\displaystyle RN\subset N}
4424:{\displaystyle r(m+N)=rm+N}
4141:Every short exact sequence
3649:{\displaystyle (ms)r=r(sm)}
3329:{\displaystyle r(sm)=(rs)m}
2749:Every short exact sequence
2080:{\displaystyle M_{1},M_{2}}
1515:such that every element of
676:if it does not contain any
5119:
4053:{\displaystyle f\circ h=g}
3367:{\displaystyle 1_{R}\,m=m}
2878:Jacobson's density theorem
2674:The contravariant functor
2653:{\displaystyle f\circ h=g}
1407:is a module that admits a
865:differential graded module
855:is the rank of the module.
782:countably generated module
29:Glossary of linear algebra
5098:Glossaries of mathematics
4832:Tensor product of modules
4361:can be made to be a left
3757:normal forms for matrices
1405:finitely presented module
1297:finitely generated module
1050:intersects non-trivially.
825:decomposition of a module
664:(frequently just complex)
4936:zero module homomorphism
4021:{\displaystyle h:P\to N}
3969:{\displaystyle f:N\to M}
3914:{\displaystyle g:P\to M}
3686:{\displaystyle m1_{R}=m}
3045:Mittag-Leffler condition
2987:Localization of a module
2621:{\displaystyle h:Y\to Q}
2569:{\displaystyle f:X\to Y}
2514:{\displaystyle g:X\to Q}
2316:{\displaystyle f:M\to M}
2290:index of an endomorphism
1994:Hilbert's syzygy theorem
1409:finite free presentation
1321:finite free presentation
1295:" is another name for a
1203:{\displaystyle rx\neq 0}
891:over a commutative ring
590:Beauville–Laszlo theorem
561:is a set of elements in
162:
5064:A course in ring theory
5006:Lam, Tsit-Yuen (1999),
4949:John A. Beachy (1999).
4731:, an additive subgroup
4506:rational canonical form
4138:is a projective module.
2087:, a group homomorphism
2000:Hilbert–Poincaré series
978:Eilenberg–Mazur swindle
35:Glossary of ring theory
4798:
4765:
4745:
4725:
4705:
4538:Restriction of scalars
4464:
4425:
4375:
4355:
4324:
4304:
4284:
4260:Quillen–Suslin theorem
4254:Quillen–Suslin theorem
4206:
4184:
4132:
4106:
4066:The covariant functor
4054:
4022:
3990:
3970:
3938:
3915:
3883:
3859:
3839:
3823:
3735:nilpotent endomorphism
3687:
3650:
3599:
3542:
3482:
3450:
3418:
3398:
3368:
3330:
3279:
3222:
3162:
3130:
3095:
3072:
2792:
2746:is a injective module.
2740:
2714:
2667:
2654:
2622:
2590:
2570:
2538:
2515:
2483:
2459:
2439:
2411:
2391:
2317:
2233:
2149:
2127:
2081:
2041:
1959:
1903:
1858:
1834:
1783:
1703:
1665:
1624:
1604:
1549:
1529:
1509:
1489:
1433:
1394:
1367:
1277:
1244:
1224:
1204:
1175:
1155:
1154:{\displaystyle r\in R}
1129:
934:
575:
555:
460:
386:
385:{\displaystyle m\in M}
357:
333:
246:
226:
157:
152:
147:
142:
137:
132:
127:
122:
117:
112:
107:
102:
97:
92:
87:
82:
77:
72:
67:
62:
57:
4799:
4766:
4746:
4726:
4706:
4465:
4426:
4376:
4356:
4325:
4305:
4285:
4207:
4185:
4133:
4107:
4055:
4023:
3996:-module homomorphism
3991:
3971:
3944:-module homomorphism
3939:
3916:
3889:-module homomorphism
3884:
3860:
3840:
3815:
3688:
3651:
3600:
3543:
3483:
3451:
3449:{\displaystyle (M,+)}
3419:
3399:
3369:
3331:
3280:
3223:
3163:
3131:
3129:{\displaystyle (M,+)}
3096:
3073:
2935:Krull–Schmidt theorem
2815:injective cogenerator
2793:
2741:
2715:
2665:
2655:
2623:
2596:-module homomorphism
2591:
2571:
2544:-module homomorphism
2539:
2516:
2489:-module homomorphism
2484:
2460:
2440:
2412:
2392:
2318:
2278:indecomposable module
2234:
2150:
2128:
2082:
2042:
2018:homological dimension
2013:homological dimension
2007:Hilbert–Serre theorem
1960:
1904:
1859:
1835:
1784:
1718:Frobenius reciprocity
1713:Frobenius reciprocity
1704:
1666:
1625:
1605:
1550:
1530:
1510:
1490:
1434:
1395:
1393:{\displaystyle F_{i}}
1368:
1327:is an exact sequence
1278:
1245:
1225:
1205:
1176:
1156:
1130:
935:
877:direct sum of modules
792:A module is called a
689:Cohen–Macaulay module
672:A module is called a
576:
556:
461:
387:
358:
334:
247:
227:
198:pure injective module
189:algebraically compact
4779:
4755:
4735:
4715:
4695:
4435:
4385:
4365:
4337:
4314:
4294:
4274:
4225:projective dimension
4196:
4145:
4122:
4070:
4032:
4000:
3980:
3948:
3928:
3893:
3873:
3849:
3829:
3661:
3610:
3556:
3496:
3460:
3428:
3424:is an abelian group
3408:
3388:
3341:
3290:
3236:
3176:
3140:
3108:
3085:
3062:
2895:Kähler differentials
2890:Kähler differentials
2753:
2730:
2678:
2632:
2600:
2580:
2548:
2528:
2493:
2473:
2449:
2429:
2401:
2327:
2295:
2161:
2139:
2091:
2051:
2031:
1913:
1868:
1848:
1793:
1773:
1693:
1642:
1614:
1594:
1539:
1519:
1499:
1447:
1423:
1377:
1331:
1254:
1234:
1214:
1185:
1181:is nontrivial (i.e.
1165:
1139:
1119:
1079:Extension of scalars
899:
733:completely reducible
565:
545:
541:A basis of a module
396:
370:
347:
256:
236:
216:
4863:torsion-free module
4814:support of a module
4495:radical of a module
4354:{\displaystyle M/N}
3701:category of modules
2970:module homomorphism
2847:Another name for a
2417:have finite length.
2002:of a graded module.
1789:over a graded ring
1315:finite presentation
1307:A module of finite
1037:essential submodule
776:countably generated
678:essential extension
641:category of modules
51:Contents:
4934:2. The
4927:1. The
4873:torsionless module
4843:topological module
4794:
4761:
4741:
4721:
4701:
4670:stably free module
4460:
4421:
4371:
4351:
4320:
4300:
4280:
4223:2. The
4202:
4180:
4128:
4102:
4050:
4018:
3986:
3966:
3934:
3911:
3879:
3855:
3835:
3824:
3683:
3646:
3595:
3538:
3478:
3456:with an operation
3446:
3414:
3394:
3364:
3326:
3275:
3218:
3158:
3136:with an operation
3126:
3091:
3068:
2954:length of a module
2843:irreducible module
2808:injective envelope
2788:
2736:
2710:
2668:
2650:
2618:
2586:
2566:
2534:
2511:
2479:
2455:
2435:
2407:
2387:
2323:is the difference
2313:
2229:
2145:
2123:
2077:
2037:
2005:3. The
1998:2. The
1955:
1899:
1888:
1854:
1830:
1819:
1779:
1699:
1661:
1620:
1600:
1545:
1525:
1505:
1485:
1441:finitely generated
1429:
1415:finitely generated
1390:
1363:
1283:is the zero ideal.
1273:
1240:
1220:
1200:
1171:
1151:
1125:
1022:enough projectives
1004:2. The
988:elementary divisor
930:
704:finitely presented
571:
551:
456:
382:
353:
329:
242:
222:
208:1. The
5073:978-0-534-13776-2
5021:978-0-387-98428-5
4991:978-0-8247-8555-0
4764:{\displaystyle M}
4744:{\displaystyle N}
4724:{\displaystyle M}
4704:{\displaystyle R}
4675:structure theorem
4659:Smith normal form
4636:semisimple module
4470:. It is called a
4374:{\displaystyle R}
4323:{\displaystyle N}
4303:{\displaystyle M}
4283:{\displaystyle R}
4205:{\displaystyle M}
4131:{\displaystyle M}
4078:
3989:{\displaystyle R}
3976:, there exists a
3937:{\displaystyle R}
3882:{\displaystyle R}
3867:projective module
3858:{\displaystyle P}
3838:{\displaystyle R}
3802:primary submodule
3747:Noetherian module
3417:{\displaystyle R}
3397:{\displaystyle M}
3094:{\displaystyle R}
3071:{\displaystyle M}
2837:invertible module
2813:3. An
2806:2. An
2739:{\displaystyle I}
2686:
2589:{\displaystyle R}
2576:, there exists a
2537:{\displaystyle R}
2482:{\displaystyle R}
2458:{\displaystyle Q}
2438:{\displaystyle R}
2410:{\displaystyle f}
2148:{\displaystyle R}
2040:{\displaystyle R}
1982:Herbrand quotient
1976:Herbrand quotient
1871:
1857:{\displaystyle M}
1802:
1782:{\displaystyle M}
1702:{\displaystyle R}
1623:{\displaystyle F}
1603:{\displaystyle R}
1548:{\displaystyle R}
1528:{\displaystyle M}
1508:{\displaystyle M}
1432:{\displaystyle M}
1261:
1250:). Equivalently,
1243:{\displaystyle M}
1223:{\displaystyle x}
1174:{\displaystyle M}
1128:{\displaystyle M}
1017:enough injectives
1006:endomorphism ring
997:1. An
771:continuous module
739:semisimple module
629:canonical divisor
574:{\displaystyle M}
554:{\displaystyle M}
514:Azumaya's theorem
440:
432:
403:
356:{\displaystyle R}
339:. It is a (left)
300:
292:
263:
245:{\displaystyle M}
225:{\displaystyle R}
5110:
5084:
5058:
5043:(3rd ed.).
5032:
5002:
4983:
4972:
4957:(1st ed.).
4956:
4803:
4801:
4800:
4795:
4770:
4768:
4767:
4762:
4750:
4748:
4747:
4742:
4730:
4728:
4727:
4722:
4710:
4708:
4707:
4702:
4603:sheaf of modules
4598:sheaf of modules
4572:Schanuel's lemma
4517:reflexive module
4469:
4467:
4466:
4461:
4430:
4428:
4427:
4422:
4380:
4378:
4377:
4372:
4360:
4358:
4357:
4352:
4347:
4329:
4327:
4326:
4321:
4310:and a submodule
4309:
4307:
4306:
4301:
4289:
4287:
4286:
4281:
4232:projective cover
4230:3. A
4211:
4209:
4208:
4203:
4189:
4187:
4186:
4181:
4167:
4137:
4135:
4134:
4129:
4111:
4109:
4108:
4103:
4086:
4085:
4080:
4079:
4076:
4059:
4057:
4056:
4051:
4027:
4025:
4024:
4019:
3995:
3993:
3992:
3987:
3975:
3973:
3972:
3967:
3943:
3941:
3940:
3935:
3920:
3918:
3917:
3912:
3888:
3886:
3885:
3880:
3864:
3862:
3861:
3856:
3844:
3842:
3841:
3836:
3692:
3690:
3689:
3684:
3676:
3675:
3655:
3653:
3652:
3647:
3604:
3602:
3601:
3596:
3547:
3545:
3544:
3539:
3487:
3485:
3484:
3479:
3455:
3453:
3452:
3447:
3423:
3421:
3420:
3415:
3403:
3401:
3400:
3395:
3381:2. A
3373:
3371:
3370:
3365:
3353:
3352:
3335:
3333:
3332:
3327:
3284:
3282:
3281:
3276:
3227:
3225:
3224:
3219:
3167:
3165:
3164:
3159:
3135:
3133:
3132:
3127:
3100:
3098:
3097:
3092:
3077:
3075:
3074:
3069:
3055:1. A
2797:
2795:
2794:
2789:
2781:
2745:
2743:
2742:
2737:
2719:
2717:
2716:
2711:
2694:
2693:
2688:
2687:
2684:
2659:
2657:
2656:
2651:
2627:
2625:
2624:
2619:
2595:
2593:
2592:
2587:
2575:
2573:
2572:
2567:
2543:
2541:
2540:
2535:
2520:
2518:
2517:
2512:
2488:
2486:
2485:
2480:
2467:injective module
2464:
2462:
2461:
2456:
2444:
2442:
2441:
2436:
2425:1. A
2416:
2414:
2413:
2408:
2396:
2394:
2393:
2388:
2322:
2320:
2319:
2314:
2238:
2236:
2235:
2230:
2228:
2227:
2154:
2152:
2151:
2146:
2135:homomorphism of
2132:
2130:
2129:
2124:
2122:
2121:
2109:
2108:
2086:
2084:
2083:
2078:
2076:
2075:
2063:
2062:
2046:
2044:
2043:
2038:
1964:
1962:
1961:
1956:
1954:
1953:
1935:
1934:
1925:
1924:
1908:
1906:
1905:
1900:
1898:
1897:
1887:
1886:
1863:
1861:
1860:
1855:
1839:
1837:
1836:
1831:
1829:
1828:
1818:
1817:
1788:
1786:
1785:
1780:
1760:global dimension
1708:
1706:
1705:
1700:
1670:
1668:
1667:
1662:
1657:
1656:
1629:
1627:
1626:
1621:
1609:
1607:
1606:
1601:
1554:
1552:
1551:
1546:
1534:
1532:
1531:
1526:
1514:
1512:
1511:
1506:
1494:
1492:
1491:
1486:
1484:
1483:
1459:
1458:
1438:
1436:
1435:
1430:
1403:2. A
1399:
1397:
1396:
1391:
1389:
1388:
1372:
1370:
1369:
1364:
1356:
1355:
1343:
1342:
1319:1. A
1282:
1280:
1279:
1274:
1263:
1262:
1259:
1249:
1247:
1246:
1241:
1229:
1227:
1226:
1221:
1209:
1207:
1206:
1201:
1180:
1178:
1177:
1172:
1160:
1158:
1157:
1152:
1134:
1132:
1131:
1126:
949:dualizing module
939:
937:
936:
931:
911:
910:
674:closed submodule
668:closed submodule
652:character module
625:canonical module
620:canonical module
585:Beauville–Laszlo
580:
578:
577:
572:
560:
558:
557:
552:
488:associated prime
482:associated prime
465:
463:
462:
457:
438:
437:
430:
405:
404:
401:
391:
389:
388:
383:
362:
360:
359:
354:
338:
336:
335:
330:
298:
297:
290:
265:
264:
261:
251:
249:
248:
243:
231:
229:
228:
223:
52:
5118:
5117:
5113:
5112:
5111:
5109:
5108:
5107:
5088:
5087:
5074:
5061:
5055:
5035:
5022:
5012:Springer-Verlag
5005:
4992:
4975:
4969:
4948:
4945:
4924:
4919:
4905:
4900:
4886:
4881:
4869:
4859:
4849:
4838:
4828:
4823:
4809:
4777:
4776:
4753:
4752:
4733:
4732:
4713:
4712:
4693:
4692:
4688:
4676:
4665:
4655:
4643:
4631:
4619:
4609:
4599:
4593:Shapiro's lemma
4589:
4578:
4568:
4563:
4534:
4524:
4512:
4502:
4490:
4485:
4472:quotient module
4433:
4432:
4383:
4382:
4363:
4362:
4335:
4334:
4312:
4311:
4292:
4291:
4272:
4271:
4267:
4255:
4250:
4239:
4194:
4193:
4160:
4143:
4142:
4120:
4119:
4073:
4068:
4067:
4030:
4029:
3998:
3997:
3978:
3977:
3946:
3945:
3926:
3925:
3891:
3890:
3871:
3870:
3847:
3846:
3827:
3826:
3808:
3798:
3786:
3774:perfect complex
3769:
3764:
3754:
3742:
3730:
3725:
3713:module spectrum
3708:
3707:module spectrum
3667:
3659:
3658:
3608:
3607:
3554:
3553:
3494:
3493:
3458:
3457:
3426:
3425:
3406:
3405:
3386:
3385:
3344:
3339:
3338:
3288:
3287:
3234:
3233:
3174:
3173:
3138:
3137:
3106:
3105:
3083:
3082:
3060:
3059:
3052:
3041:
3031:
3021:
3016:
2997:modules, where
2983:
2977:Linear topology
2965:
2949:
2944:
2930:
2920:
2912:
2901:
2891:
2886:
2874:
2869:
2856:
2844:
2832:
2822:
2774:
2751:
2750:
2728:
2727:
2681:
2676:
2675:
2630:
2629:
2598:
2597:
2578:
2577:
2546:
2545:
2526:
2525:
2491:
2490:
2471:
2470:
2447:
2446:
2427:
2426:
2422:
2399:
2398:
2325:
2324:
2293:
2292:
2285:
2273:
2261:
2256:
2244:
2219:
2159:
2158:
2137:
2136:
2113:
2100:
2089:
2088:
2067:
2054:
2049:
2048:
2029:
2028:
2024:
2014:
1989:
1977:
1972:
1939:
1926:
1916:
1911:
1910:
1889:
1866:
1865:
1846:
1845:
1820:
1791:
1790:
1771:
1770:
1766:
1756:
1744:
1732:
1727:
1714:
1691:
1690:
1682:
1676:
1648:
1640:
1639:
1612:
1611:
1592:
1591:
1587:
1577:
1571:Fitting's lemma
1560:
1537:
1536:
1517:
1516:
1497:
1496:
1475:
1450:
1445:
1444:
1421:
1420:
1416:
1380:
1375:
1374:
1347:
1334:
1329:
1328:
1316:
1304:
1288:
1252:
1251:
1232:
1231:
1212:
1211:
1183:
1182:
1163:
1162:
1137:
1136:
1117:
1116:
1114:faithful module
1109:
1104:
1075:
1065:
1055:
1031:Given a module
1028:
1013:
994:
984:
974:
973:Eilenberg–Mazur
969:
960:Drinfeld module
955:
945:
902:
897:
896:
884:
872:
860:
840:
835:dense submodule
832:
820:
808:
803:
789:
777:
767:
757:
746:
737:Synonymous to "
734:
723:
711:
700:coherent module
695:
685:
669:
658:
648:
636:
621:
616:
604:
596:
586:
563:
562:
543:
542:
538:
532:balanced module
528:
523:
510:
494:
483:
476:Artinian module
471:
394:
393:
368:
367:
345:
344:
254:
253:
234:
233:
214:
213:
205:
190:
185:
180:
179:
178:
177:
53:
50:
12:
11:
5:
5116:
5114:
5106:
5105:
5100:
5090:
5089:
5086:
5085:
5072:
5059:
5053:
5045:Addison-Wesley
5033:
5020:
5003:
4990:
4973:
4967:
4959:Addison-Wesley
4944:
4941:
4940:
4939:
4932:
4925:
4922:
4918:
4915:
4912:
4911:
4909:weak dimension
4906:
4903:
4899:
4896:
4895:
4894:
4891:uniform module
4887:
4884:
4880:
4877:
4876:
4875:
4870:
4867:
4865:
4860:
4857:
4855:
4850:
4847:
4845:
4839:
4836:
4834:
4829:
4826:
4822:
4819:
4818:
4817:
4810:
4807:
4805:
4793:
4790:
4787:
4784:
4760:
4740:
4720:
4700:
4689:
4686:
4684:
4677:
4674:
4672:
4666:
4663:
4661:
4656:
4653:
4651:
4644:
4641:
4639:
4632:
4629:
4627:
4620:
4617:
4615:
4610:
4607:
4605:
4600:
4597:
4595:
4590:
4587:
4585:
4579:
4576:
4574:
4569:
4566:
4562:
4559:
4558:
4557:
4535:
4532:
4530:
4525:
4522:
4520:
4513:
4510:
4508:
4503:
4500:
4498:
4491:
4488:
4484:
4481:
4480:
4479:
4459:
4456:
4453:
4449:
4446:
4443:
4440:
4420:
4417:
4414:
4411:
4408:
4405:
4402:
4399:
4396:
4393:
4390:
4370:
4350:
4346:
4342:
4332:quotient group
4319:
4299:
4279:
4268:
4265:
4263:
4256:
4253:
4249:
4246:
4245:
4243:pure submodule
4240:
4238:pure submodule
4237:
4235:
4228:
4221:
4220:
4219:
4218:
4215:
4214:
4213:
4201:
4191:
4179:
4176:
4173:
4170:
4166:
4163:
4159:
4156:
4153:
4150:
4139:
4127:
4117:
4101:
4098:
4095:
4092:
4089:
4084:
4049:
4046:
4043:
4040:
4037:
4017:
4014:
4011:
4008:
4005:
3985:
3965:
3962:
3959:
3956:
3953:
3933:
3910:
3907:
3904:
3901:
3898:
3878:
3854:
3834:
3809:
3806:
3804:
3799:
3796:
3794:
3787:
3784:
3782:
3780:perfect module
3778:2.
3776:
3772:1.
3770:
3767:
3763:
3760:
3759:
3758:
3755:
3752:
3750:
3743:
3740:
3738:
3731:
3728:
3724:
3721:
3720:
3709:
3706:
3704:
3697:
3696:
3695:
3694:
3693:
3682:
3679:
3674:
3670:
3666:
3656:
3645:
3642:
3639:
3636:
3633:
3630:
3627:
3624:
3621:
3618:
3615:
3605:
3594:
3591:
3588:
3585:
3582:
3579:
3576:
3573:
3570:
3567:
3564:
3561:
3550:
3549:
3537:
3534:
3531:
3528:
3525:
3522:
3519:
3516:
3513:
3510:
3507:
3504:
3501:
3477:
3474:
3471:
3468:
3465:
3445:
3442:
3439:
3436:
3433:
3413:
3404:over the ring
3393:
3379:
3378:
3377:
3376:
3375:
3374:
3363:
3360:
3357:
3351:
3347:
3336:
3325:
3322:
3319:
3316:
3313:
3310:
3307:
3304:
3301:
3298:
3295:
3285:
3274:
3271:
3268:
3265:
3262:
3259:
3256:
3253:
3250:
3247:
3244:
3241:
3230:
3229:
3217:
3214:
3211:
3208:
3205:
3202:
3199:
3196:
3193:
3190:
3187:
3184:
3181:
3157:
3154:
3151:
3148:
3145:
3125:
3122:
3119:
3116:
3113:
3090:
3067:
3053:
3050:
3048:
3042:
3040:Mittag-Leffler
3039:
3037:
3032:
3029:
3027:
3022:
3019:
3015:
3012:
3011:
3010:
2984:
2981:
2979:
2975:2.
2973:
2966:
2963:
2961:
2950:
2947:
2943:
2940:
2939:
2938:
2931:
2928:
2926:
2924:Koszul complex
2921:
2919:Koszul complex
2918:
2916:
2913:
2910:
2908:
2902:
2899:
2897:
2892:
2889:
2885:
2882:
2881:
2880:
2875:
2872:
2868:
2865:
2864:
2857:
2854:
2852:
2845:
2842:
2840:
2833:
2830:
2828:
2823:
2820:
2818:
2811:
2804:
2803:
2802:
2801:
2800:
2799:
2787:
2784:
2780:
2777:
2773:
2770:
2767:
2764:
2761:
2758:
2747:
2735:
2725:
2709:
2706:
2703:
2700:
2697:
2692:
2649:
2646:
2643:
2640:
2637:
2617:
2614:
2611:
2608:
2605:
2585:
2565:
2562:
2559:
2556:
2553:
2533:
2510:
2507:
2504:
2501:
2498:
2478:
2454:
2434:
2423:
2420:
2418:
2406:
2386:
2383:
2380:
2377:
2374:
2371:
2368:
2365:
2362:
2359:
2356:
2353:
2350:
2347:
2344:
2341:
2338:
2335:
2332:
2312:
2309:
2306:
2303:
2300:
2286:
2283:
2281:
2274:
2272:indecomposable
2271:
2269:
2262:
2259:
2255:
2252:
2251:
2250:
2245:
2242:
2240:
2226:
2222:
2218:
2215:
2212:
2209:
2206:
2203:
2200:
2196:
2193:
2190:
2187:
2184:
2181:
2178:
2175:
2172:
2169:
2166:
2144:
2120:
2116:
2112:
2107:
2103:
2099:
2096:
2074:
2070:
2066:
2061:
2057:
2036:
2025:
2022:
2020:
2015:
2012:
2010:
2003:
1996:
1992:1.
1990:
1987:
1985:
1978:
1975:
1971:
1968:
1967:
1966:
1952:
1949:
1946:
1942:
1938:
1933:
1929:
1923:
1919:
1896:
1892:
1885:
1881:
1878:
1874:
1853:
1827:
1823:
1816:
1812:
1809:
1805:
1801:
1798:
1778:
1767:
1764:
1762:
1757:
1754:
1752:
1749:generating set
1745:
1743:generating set
1742:
1740:
1733:
1730:
1726:
1723:
1722:
1721:
1715:
1712:
1710:
1698:
1683:
1680:
1678:
1660:
1655:
1651:
1647:
1636:tensor product
1619:
1599:
1588:
1585:
1583:
1578:
1575:
1573:
1569:2.
1567:
1563:1.
1561:
1558:
1556:
1544:
1524:
1504:
1482:
1478:
1474:
1471:
1468:
1465:
1462:
1457:
1453:
1428:
1417:
1414:
1412:
1401:
1387:
1383:
1362:
1359:
1354:
1350:
1346:
1341:
1337:
1317:
1314:
1312:
1305:
1302:
1300:
1289:
1286:
1284:
1272:
1269:
1266:
1239:
1219:
1199:
1196:
1193:
1190:
1170:
1150:
1147:
1144:
1124:
1110:
1107:
1103:
1100:
1099:
1098:
1076:
1073:
1071:
1066:
1063:
1061:
1059:exact sequence
1056:
1053:
1051:
1029:
1026:
1024:
1019:
1014:
1011:
1009:
1002:
995:
992:
990:
985:
982:
980:
975:
972:
968:
965:
964:
963:
956:
953:
951:
946:
943:
941:
929:
926:
923:
920:
917:
914:
909:
905:
895:is the module
885:
882:
880:
873:
870:
868:
861:
858:
856:
841:
838:
836:
833:
830:
828:
821:
818:
816:
809:
806:
802:
799:
798:
797:
790:
787:
785:
778:
775:
773:
768:
765:
763:
758:
755:
753:
747:
744:
742:
735:
732:
730:
728:compact module
724:
721:
719:
712:
709:
707:
696:
693:
691:
686:
684:Cohen–Macaulay
683:
681:
670:
667:
665:
659:
656:
654:
649:
646:
644:
637:
634:
632:
622:
619:
615:
612:
611:
610:
605:
602:
600:
597:
594:
592:
587:
584:
582:
570:
550:
539:
536:
534:
529:
526:
522:
519:
518:
517:
511:
508:
506:
495:
492:
490:
486:1.
484:
481:
479:
472:
469:
467:
455:
452:
449:
446:
443:
436:
429:
426:
423:
420:
417:
414:
411:
408:
381:
378:
375:
364:
352:
328:
325:
322:
319:
316:
312:
309:
306:
303:
296:
289:
286:
283:
280:
277:
274:
271:
268:
241:
221:
206:
203:
201:
191:
188:
184:
181:
176:
175:
170:
165:
160:
155:
150:
145:
140:
135:
130:
125:
120:
115:
110:
105:
100:
95:
90:
85:
80:
75:
70:
65:
60:
54:
49:
48:
46:
13:
10:
9:
6:
4:
3:
2:
5115:
5104:
5103:Module theory
5101:
5099:
5096:
5095:
5093:
5083:
5079:
5075:
5069:
5065:
5060:
5056:
5054:0-201-55540-9
5050:
5046:
5042:
5038:
5034:
5031:
5027:
5023:
5017:
5013:
5009:
5004:
5001:
4997:
4993:
4987:
4982:
4981:
4974:
4970:
4968:0-521-64407-0
4964:
4960:
4955:
4954:
4947:
4946:
4942:
4937:
4933:
4930:
4926:
4921:
4916:
4914:
4910:
4907:
4902:
4897:
4892:
4888:
4883:
4878:
4874:
4871:
4866:
4864:
4861:
4856:
4854:
4851:
4846:
4844:
4840:
4835:
4833:
4830:
4825:
4820:
4815:
4811:
4806:
4791:
4788:
4785:
4782:
4774:
4758:
4738:
4718:
4698:
4690:
4685:
4682:
4678:
4673:
4671:
4667:
4662:
4660:
4657:
4652:
4649:
4648:simple module
4645:
4640:
4637:
4633:
4628:
4625:
4621:
4616:
4614:
4611:
4606:
4604:
4601:
4596:
4594:
4591:
4586:
4583:
4582:Schur's lemma
4580:
4575:
4573:
4570:
4565:
4560:
4555:
4551:
4547:
4543:
4539:
4536:
4531:
4529:
4526:
4521:
4518:
4514:
4509:
4507:
4504:
4499:
4496:
4492:
4487:
4482:
4477:
4476:factor module
4473:
4457:
4454:
4451:
4447:
4444:
4441:
4438:
4418:
4415:
4412:
4409:
4406:
4400:
4397:
4394:
4388:
4368:
4348:
4344:
4340:
4333:
4317:
4297:
4277:
4270:Given a left
4269:
4264:
4261:
4257:
4252:
4247:
4244:
4241:
4236:
4233:
4229:
4226:
4222:
4216:
4199:
4192:
4177:
4171:
4164:
4161:
4154:
4148:
4140:
4125:
4118:
4115:
4096:
4093:
4090:
4082:
4065:
4064:
4062:
4061:
4047:
4044:
4041:
4038:
4035:
4015:
4009:
4006:
4003:
3983:
3963:
3957:
3954:
3951:
3931:
3924:
3908:
3902:
3899:
3896:
3876:
3868:
3852:
3832:
3821:
3820:
3814:
3810:
3805:
3803:
3800:
3795:
3792:
3788:
3783:
3781:
3777:
3775:
3771:
3766:
3761:
3756:
3751:
3748:
3744:
3739:
3736:
3732:
3727:
3722:
3718:
3714:
3710:
3705:
3702:
3698:
3680:
3677:
3672:
3668:
3664:
3657:
3640:
3637:
3631:
3628:
3625:
3619:
3616:
3606:
3592:
3589:
3586:
3583:
3580:
3577:
3574:
3568:
3565:
3562:
3552:
3551:
3535:
3532:
3529:
3526:
3523:
3517:
3514:
3511:
3508:
3505:
3502:
3492:
3491:
3490:
3489:
3475:
3469:
3466:
3463:
3440:
3437:
3434:
3411:
3391:
3384:
3380:
3361:
3358:
3355:
3349:
3345:
3337:
3323:
3317:
3314:
3308:
3302:
3299:
3293:
3286:
3272:
3269:
3266:
3263:
3260:
3257:
3251:
3248:
3245:
3239:
3232:
3231:
3215:
3212:
3209:
3206:
3203:
3197:
3194:
3191:
3188:
3185:
3182:
3172:
3171:
3170:
3169:
3155:
3149:
3146:
3143:
3120:
3117:
3114:
3104:
3103:abelian group
3088:
3081:
3065:
3058:
3054:
3049:
3046:
3043:
3038:
3036:
3033:
3028:
3026:
3025:Matlis module
3023:
3020:Matlis module
3018:
3013:
3008:
3004:
3000:
2996:
2992:
2988:
2985:
2980:
2978:
2974:
2971:
2967:
2962:
2959:
2955:
2951:
2946:
2941:
2936:
2932:
2929:Krull–Schmidt
2927:
2925:
2922:
2917:
2914:
2909:
2906:
2903:
2898:
2896:
2893:
2888:
2883:
2879:
2876:
2871:
2866:
2862:
2858:
2853:
2850:
2849:simple module
2846:
2841:
2838:
2834:
2829:
2827:
2824:
2819:
2816:
2812:
2809:
2805:
2785:
2778:
2775:
2768:
2762:
2756:
2748:
2733:
2726:
2723:
2704:
2701:
2698:
2690:
2673:
2672:
2670:
2669:
2664:
2647:
2644:
2641:
2638:
2635:
2615:
2609:
2606:
2603:
2583:
2563:
2557:
2554:
2551:
2531:
2524:
2508:
2502:
2499:
2496:
2476:
2468:
2465:is called an
2452:
2432:
2424:
2419:
2404:
2378:
2372:
2369:
2363:
2360:
2357:
2348:
2342:
2339:
2333:
2330:
2310:
2304:
2301:
2298:
2291:
2287:
2282:
2279:
2275:
2270:
2267:
2263:
2258:
2253:
2249:
2246:
2241:
2224:
2220:
2216:
2213:
2210:
2207:
2204:
2201:
2191:
2188:
2182:
2179:
2173:
2167:
2164:
2156:
2142:
2118:
2114:
2105:
2101:
2097:
2094:
2072:
2068:
2064:
2059:
2055:
2034:
2027:For two left
2026:
2021:
2019:
2016:
2011:
2008:
2004:
2001:
1997:
1995:
1991:
1986:
1983:
1979:
1974:
1969:
1950:
1947:
1944:
1940:
1936:
1931:
1927:
1921:
1917:
1894:
1890:
1879:
1876:
1872:
1851:
1843:
1842:graded module
1825:
1821:
1810:
1807:
1803:
1799:
1796:
1776:
1768:
1763:
1761:
1758:
1753:
1750:
1746:
1741:
1738:
1737:Galois module
1734:
1729:
1724:
1719:
1716:
1711:
1696:
1688:
1684:
1679:
1674:
1658:
1653:
1649:
1645:
1637:
1633:
1617:
1597:
1589:
1584:
1582:
1579:
1574:
1572:
1568:
1566:
1565:fitting ideal
1562:
1557:
1542:
1522:
1502:
1480:
1476:
1472:
1469:
1466:
1463:
1460:
1455:
1451:
1442:
1426:
1418:
1413:
1410:
1406:
1402:
1385:
1381:
1360:
1352:
1348:
1339:
1335:
1326:
1322:
1318:
1313:
1310:
1306:
1303:finite length
1301:
1298:
1294:
1293:finite module
1290:
1285:
1267:
1237:
1217:
1197:
1194:
1191:
1188:
1168:
1148:
1145:
1142:
1122:
1115:
1111:
1106:
1101:
1096:
1092:
1088:
1084:
1080:
1077:
1072:
1070:
1067:
1062:
1060:
1057:
1052:
1049:
1045:
1041:
1038:
1034:
1030:
1025:
1023:
1020:
1018:
1015:
1010:
1007:
1003:
1000:
996:
991:
989:
986:
981:
979:
976:
971:
966:
961:
957:
952:
950:
947:
942:
924:
921:
918:
912:
907:
903:
894:
890:
886:
881:
878:
874:
869:
866:
862:
857:
854:
850:
846:
842:
837:
834:
829:
826:
822:
819:decomposition
817:
814:
810:
805:
800:
795:
794:cyclic module
791:
786:
783:
779:
774:
772:
769:
764:
762:
759:
754:
751:
748:
743:
740:
736:
731:
729:
725:
720:
717:
713:
708:
705:
701:
697:
692:
690:
687:
682:
679:
675:
671:
666:
663:
662:chain complex
660:
657:chain complex
655:
653:
650:
645:
642:
638:
633:
630:
626:
623:
618:
613:
609:
606:
601:
598:
593:
591:
588:
583:
568:
548:
540:
535:
533:
530:
525:
520:
515:
512:
507:
504:
500:
496:
491:
489:
485:
480:
477:
473:
468:
450:
447:
444:
441:
427:
424:
421:
415:
409:
379:
376:
373:
365:
350:
342:
323:
320:
317:
310:
307:
304:
301:
287:
284:
281:
275:
269:
239:
219:
211:
207:
202:
199:
196:(also called
195:
192:
187:
182:
174:
171:
169:
166:
164:
161:
159:
156:
154:
151:
149:
146:
144:
141:
139:
136:
134:
131:
129:
126:
124:
121:
119:
116:
114:
111:
109:
106:
104:
101:
99:
96:
94:
91:
89:
86:
84:
81:
79:
76:
74:
71:
69:
66:
64:
61:
59:
56:
55:
45:
43:
42:
37:
36:
31:
30:
24:
22:
18:
17:Module theory
5063:
5040:
5007:
4979:
4952:
4913:
4858:torsion-free
4553:
4552:-modules to
4549:
4545:
4541:
4475:
3865:is called a
3817:
3383:right module
3006:
3003:localization
2998:
2994:
2990:
2982:localization
2023:homomorphism
1630:is called a
1324:
1323:of a module
1094:
1093:-modules to
1090:
1086:
1082:
1047:
1043:
1039:
1032:
999:endomorphism
993:endomorphism
892:
888:
859:differential
852:
848:
503:endomorphism
499:automorphism
493:automorphism
39:
33:
27:
25:
15:
4929:zero module
4868:torsionless
4853:Tor functor
4837:topological
4664:stably free
4613:snake lemma
4548:to convert
4533:restriction
4381:-module by
3869:if given a
3057:left module
2993:modules to
2861:isomorphism
2855:isomorphism
2469:if given a
2248:Hom functor
1687:free module
1632:flat module
1089:to convert
1069:Ext functor
1064:Ext functor
883:dual module
845:determinant
839:determinant
756:composition
752:of a module
392:is the set
252:is the set
210:annihilator
204:annihilator
5092:Categories
5037:Serge Lang
4943:References
4630:semisimple
4528:resolution
4523:resolution
4028:such that
3923:surjective
3807:projective
3741:Noetherian
2831:invertible
2826:invariants
2628:such that
2266:idempotent
2260:idempotent
2133:is called
1581:Five lemma
1291:The term "
983:elementary
871:direct sum
766:continuous
750:completion
745:completion
212:of a left
173:References
26:See also:
4789:⊂
4773:submodule
4687:submodule
4556:-modules.
4511:reflexive
4455:∈
4442:∈
4190:is split.
4175:→
4169:→
4158:→
4152:→
4097:−
4039:∘
4013:→
3961:→
3906:→
3785:principal
3729:nilpotent
3533:∈
3521:∀
3512:∈
3500:∀
3473:→
3467:×
3213:∈
3201:∀
3192:∈
3180:∀
3153:→
3147:×
3078:over the
2989:converts
2958:dimension
2900:Kaplansky
2821:invariant
2798:is split.
2783:→
2772:→
2766:→
2760:→
2699:−
2639:∘
2613:→
2561:→
2523:injective
2521:, and an
2506:→
2421:injective
2373:
2364:
2358:−
2343:
2334:
2308:→
2217:∈
2205:∈
2199:∀
2183:ϕ
2168:ϕ
2111:→
2095:ϕ
2047:-modules
1937:⊆
1880:∈
1873:⨁
1811:∈
1804:⨁
1769:A module
1650:⊗
1646:−
1419:A module
1358:→
1345:→
1210:for some
1195:≠
1146:∈
1097:-modules.
1074:extension
1027:essential
944:dualizing
913:
647:character
425:∈
377:∈
321:∈
315:∀
285:∈
5039:(1993).
4711:-module
4691:Given a
4567:Schanuel
4501:rational
4290:-module
4266:quotient
4165:′
3921:, and a
3845:-module
3717:spectrum
2873:Jacobson
2779:′
2445:-module
2155:-modules
1638:functor
1610:-module
1108:faithful
954:Drinfeld
813:D-module
716:cokernel
710:cokernel
694:coherent
635:category
608:bimodule
603:bimodule
527:balanced
470:Artinian
232:-module
168:See also
5082:1096302
5041:Algebra
5030:1653294
5000:1201818
4885:uniform
4808:support
4588:Shapiro
4489:radical
3819:lifting
3797:primary
3768:perfect
1988:Hilbert
1634:if the
1559:fitting
722:compact
509:Azumaya
21:modules
5080:
5070:
5051:
5028:
5018:
4998:
4988:
4965:
4827:tensor
4642:simple
4330:, the
3753:normal
3101:is an
3051:module
2964:linear
2948:length
2911:kernel
2361:length
2331:length
1765:graded
1755:global
1731:Galois
1373:where
1309:length
1287:finite
1012:enough
788:cyclic
501:is an
439:
431:
299:
291:
4771:is a
4654:Smith
4624:socle
4618:socle
4608:snake
4577:Schur
4114:exact
3715:is a
3001:is a
2722:exact
2340:coker
2284:index
1840:is a
1673:exact
1054:exact
1035:, an
831:dense
537:basis
341:ideal
5068:ISBN
5049:ISBN
5016:ISBN
4986:ISBN
4963:ISBN
4923:zero
4904:weak
4812:The
4679:The
4622:The
4493:The
4431:for
4258:The
3080:ring
3047:(ML)
2952:The
2933:The
2288:The
1909:and
1681:free
1586:flat
1576:five
843:The
714:The
639:The
4848:Tor
4775:if
4751:of
4544:to
4474:or
4112:is
4077:Hom
3005:of
2859:An
2835:An
2720:is
2685:Hom
2370:ker
2276:An
2264:An
2243:Hom
2157:if
1844:if
1671:is
1495:in
1439:is
1260:Ann
1230:in
1161:on
1085:to
1042:of
904:Hom
595:big
497:An
474:An
402:Ann
343:of
262:Ann
163:XYZ
5094::
5078:MR
5076:,
5047:.
5026:MR
5024:,
5014:,
4996:MR
4994:,
4961:.
4889:A
4841:A
4668:A
4646:A
4634:A
4515:A
4060:.
3825:A
3789:A
3745:A
3733:A
3711:A
2660:.
1980:A
1735:A
1685:A
1590:A
1112:A
958:A
875:A
863:A
823:A
811:A
780:A
741:".
726:A
698:A
416::=
276::=
44:.
38:,
32:,
5057:.
4971:.
4917:Z
4898:W
4879:U
4821:T
4804:.
4792:N
4786:N
4783:R
4759:M
4739:N
4719:M
4699:R
4561:S
4554:R
4550:S
4546:S
4542:R
4483:R
4478:.
4458:M
4452:m
4448:,
4445:R
4439:r
4419:N
4416:+
4413:m
4410:r
4407:=
4404:)
4401:N
4398:+
4395:m
4392:(
4389:r
4369:R
4349:N
4345:/
4341:M
4318:N
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4278:R
4248:Q
4200:M
4178:0
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4162:L
4155:L
4149:0
4126:M
4116:.
4100:)
4094:,
4091:P
4088:(
4083:R
4048:g
4045:=
4042:h
4036:f
4016:N
4010:P
4007::
4004:h
3984:R
3964:M
3958:N
3955::
3952:f
3932:R
3909:M
3903:P
3900::
3897:g
3877:R
3853:P
3833:R
3822:.
3762:P
3723:N
3703:.
3681:m
3678:=
3673:R
3669:1
3665:m
3644:)
3641:m
3638:s
3635:(
3632:r
3629:=
3626:r
3623:)
3620:s
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3614:(
3593:r
3590:n
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3530:n
3527:,
3524:m
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3509:s
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3318:s
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2604:h
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2060:1
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1970:H
1965:.
1951:j
1948:+
1945:i
1941:M
1932:j
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1922:i
1918:A
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