Talk:Outline of algebraic structures

830:

old content from Knowledge altogether (I know it is still available in the page history, that's not my point). Basically I want to know where the content of the old page should go (on Knowledge). When you say above that "nobody is going to read it", I both agree and disagree: I agree with the sentiment that most won't read it, but disagree as I am one of the few that really did read it, in detail. Anyways: I am not against the changes that have been done, they might even be an improvement of this page. What I am really after is a proper location for the old content.

1012:

this structure," which obviously clashes with the section heading. To avoid this minor problem, I moved this entry to a new section dedicated to algebraic structures with two sets and four operations. Another example: I transferred the Hazewinkel reference from "External links" to "References," where it belongs. Another example: I made the introduction crisper by transferring some material further down and rewording a few sentences. Which of these changes made you reject the entire edit?

1041:" is short for "hierarchical outline". There are two types of outlines: sentence outlines (like those you made in school to plan a paper), and topic outlines (like the topical synopses that professors hand out at the beginning of a college course). Outlines on Knowledge are primarily topic outlines that serve 2 main purposes: they provide taxonomical classification of subjects showing what topics belong to a subject and how they are related to each other (via their placement in the 74: 53: 22: 933: 429:, and my preference is to include in this list every structure described somewhere in Knowledge. And thus I created a paragraph describing free modules. It is true that there is a free variant of all sorts of algebraic structures, and perhaps this entry should include 1-4 sentences talking about that. Are free algebras properly discussed anywhere in Wiki? 230:, do have formal axiomatic structures, although the presentation of those structures in texts I can access leaves something to be desired. Birkhoff and MacLane give these fair attention. Clifford and geometric algebras excite physicists. I am drawn to exterior algebra because fascinated by their inventor, 975:

Hi! I saw you made an extremely large edit containing some good changes recently. Unfortunately, there were also a lot of questionable changes mixed in. Since the edit was too monolithic to split between the two types, I have reverted it and requested your presence here. It would be nice to carry out

829:

I used to come to this page all the time for its encyclopedic (ha!) nature. I feel that it has now been gutted. I **liked** the huge list, especially the inclusion of non-standard items. I am not against make this page an 'outline' based on fairly stable content -- I am against the deletion of the

442:

Let me try to explain what's going on with free algebras. The concept of a free X isn't a "variant" of the concept of an X in the same way a commutative X or an X-with-identity is. Free groups are, for example, comparable to alternating groups. Yes, we can talk about alternating groups in the plural,

1011:

What specific changes pose you a problem? I did not change the semantics anywhere. I just tried to improve the wording and fixed a few simple classification problems. For instance, in Section "Three binary operations and two sets," the entry "Bialgebra" states "There are actually four operations for

787:

for those who care to try to read it. The outline can certainly regain structures that were removed, but we really need to avoid including every single name and detail about every structure that can be found. Not only is it an eyesore, but also nobody is going to read it. According to the guidelines

480:

of finite order. It is simply a concrete instance of a group and not a distinct algebraic structure. Hence what makes an alternating group distinct from other groups is not its universal algebra structure (the variety group includes alternating groups), but its model theoretic structure. So I see no

420:

Let me return to free modules. It is very curious (to me) that modules are varieties but that free modules are not. My orginal description a module mentioned an optional basis. An editor objected that there is no module analog of a vector space basis. A bit of browsing of Birkhoff and MacLane, and I

887:

to make it more accessible and less rambling. Moving any information from the outline would cause duplication and reintroduction of the very problems that were being addressed. While the articles of course share content, the missions of outlines are very different from those of regular articles, so

721:

Hi. I'm guessing many of the problems I am about to mention are probably a result of the "list/outline" switch done earlier. I think the article does not carry out the first "main purpose of outlines" (1. present subtopics...provide understanding especially to those unfamiliar with the topic.) This

281:

mentions "pointed unary systems" and then stops; I immediately saw that it was only one small step short of a Peano system. Then why not Peano arithmetic? And thus the whole section titled Arithmetic was born. I am having trouble getting a handle on Skolem arithmetic, so much so that I have Emailed

1068:

is missing from the list. Since it shares many properties with module-like structures, such as being a set acting in another, such as vector space wich is a field acting in "the vector set" or module wich is a ring acting on "the modules", the group action is a group acting on a set. Now, the set

208:

is a variety, and you can check that the axioms are all identities. To keep it simple, a vector space over the field with 2 elements is a set with one 0-ary operation (the zero vector), three unary operations (additive inverse, multiply by 0, and multiply by 1) and one binary operation (addition).

237:

BTW, I noticed only 30 minutes ago that you killed my paragraph on free modules. I wrote that paragraph to answer objections someone raised 6-8 weeks ago, carefully distilling it from Birkhoff and MacLane. I was rather proud of the result. As far as I could determine, Knowledge does not do free

155:

Melchior, thank you for taking an interest in this entry. You have materially changed the stuff on modules, vector spaces, algebras over rings/fields, in ways I have no grounds to dispute. I refined lots of details using Birkhoff and MacLane (and Herget and Michel), but the fact remains I am no

166:

Jipsen confirms that vector spaces form a variety, but I do not see how, given that the real field is not a variety. I have not yet fully grasped just what it means for a structure to be a variety, and so the discussion at the start of section 2, re axioms that are not identities, will have to

1015:

Feel free to keep the section headings unchanged. I proposed to replace "N operations on/and M sets" with "M sets and N operations" because Lang, Hungerford, Rotman, Bourbaki, etc. all define algebraic structures as sets with operations, rather than operations on sets. Mentioning sets before

371:

Heh, I'm afraid that rather inelegant legacy is partially mine; I created the section to deal with sets with structure other than operations that had been included by a still earlier editor. Such is the evolution of an article... Probably it should be recombined with "Structures that are not

302:

185:; there are suprisingly few books on the subject, the ones I have handy are less than pellucid, and the relevant Wiki entries don't meet my standard of clarity either. Finally, I am disappointed that we cannot agree on a home for that creature taught to undergraduates everywhere, called 987:

Massive rewordings of text by a single author are usually viewed with suspicion because they may be heavily influenced by personal views. I don't mean to say you can't write anything like that, but it would be more constructive if we could do a chunk at a time and not every section at

222:

I am reluctant to agree. Linear algebra is vector spaces plus linear transformations over vector spaces, as characterized by matrices and determinants. I have been rather surprised to discover that the literature is silent about any formal axiomatic structure for matrices and

803:

Since the subtopics in outlines are linked whenever Knowledge has articles about them, outlines serve as a table of contents or site map to its subject's coverage on Knowledge. In this respect, each outline is a navigation aid, for its subject and Knowledge's coverage of

203:

vector spaces together don't form a variety, or really even a sensible category of any kind. After, all, what would a "linear map" between a vector space over the reals and a vector space over the field with 7 elements look like? But the category of vector spaces

249:

does not state any freeness conditions. Second, every algebraic structure in the variety section has a free algebra concept, so why should modules be given an extra entry for theirs? It's better to keep this list concise and do full justice to the concept at the

845:

Hi, thanks for making your request so understandable. Firstly, if you can recommend items that got the axe that you would like to see back again, I would be happy to try to fit some back in, provided they seem to be a reasonably established terms. I did cut the

811:

I'm contending that the previous article was bungling #1 by including too much material and organizing it in an oversophisticated way. We should strive to keep the organization as simple as possible, and minimize the space taken up by overly obscure structures.

156:

authority whatsoever; in higher math and logic, I am wholly self-taught. I come to this topic fascinated by Boolean algebra and lattices, and with a working knowledge of linear algebra. Otherwise, I pretty much only reword what I find in printed sources.

913:

has (as it should) trees of these topics. Would it be prudent / in-style to remove the former's flat-lists, and simply point readers of the former to the trees of topics in the latter? (Excuse me, I'm new to both higher math and editing Knowledge.)

214:

As for "multilinear algebra" and "linear algebra", these aren't algebraic structures, so they don't merit entries in a list of algebraic structures. They're just fields of study, like universal algebra, abstract algebra, and middle-school

730:

Remove the big list of examples. It does not seem appropriate on an outline, and they are certainly present in all the articles for which the outline acts as a navigation tool. A handful of elementary examples might be well-placed in the

799:

Since outlines present a subject's subtopics and how they are related to each other by where they are placed on the outline's tree structure, outlines provide understanding, especially to those who are not completely familiar with the

983:

You changed a lot of headers from something like "Two X's and two Y's" to "Two Y'x and two X's". I suppose this is possible, but superficially it seems like a change that doesn't do anything. I could be persuaded,

269:

I think the main editorial value of the variety/nonvariety dichotomy is that the variety section has a clear and unambiguous circumscription, while the nonvariety section is undefined and can contain practically

740:

Relegate the variety/nonvariety split to a subsection on universal algebra. The organization of objects should be less Linnean and more conceptual, as was recently implemented in Template:Algebraic structure.

691:

First, it is true that one- and two-sorted structures account for the bulk of algebraic structures that appear in mathematics (e.g. groups are one-sorted, vector spaces two-sorted). But why not allow more

432:

Jipsen mentions structures that I don't quite know how to pigeonhole: hoops come to mind. But all such structures in Jipsen have no Wiki entry to date, so I omit them from this list with a clear conscience!

726:

A brief intro about the presence of algebraic objects in mathematics, and a description about how they are usually presented (first groups, fields and vector spaces, and lattices, only later the harder

133: 524:

Matroids and antimatroids are pretty clearly not varieties. Do they belong here and if so, where? I have put them under lattices that are not varieties, but am very open to moving them elsewhere.

277:

True, although I am quite comfortable with the scope of the entry as it now stands. I did give thought to adding Hilbert and Banach spaces, the topological spaces T0, T1, and T2... and blinked.

163:

as it stood 4+ months ago. (Incidentally, Stan Burris is quite annoyed by the Wiki definition of "algebraic structure.") The whole variety/nonvariety dichotomy is another legacy from the past.

948:

guidelines seem to encourage. Since you've drawn my attention to the outline again, I've decided to start working on making the outline a little more useful (I had almost forgotten about it!)

498:

Would someone well-versed in combinatory logic give my definition of combinatory algebra a close critical reading? The combinatory logic I am to algebraize is, of course, the classic one with

853:

I don't think that any portion of WP would be a good home for the excessive detail and terms of dubious commonality would be welcome. Let's see if we can replant a bit of what was lost here.

377:

I would be fine with combining them, as long as there remains a clear visual distinction between the two: perhaps colored flags for the entries? Melchoir 07:13, 18 July 2006 (UTC)

734:

There are nonstandard appearing which could be mistaken for standard. Two examples: "ringoid" and "shell". The shell article has even been created and deleted by WP:Math already.

177:

The definition of a structure given in this entry must be consistent with the definition given in the linked Wiki entry. If that entry is wrong, that should be addressed first.

743:

I know "outlines are not lists" but certainly part of this outline will end up being a list, out of necessity. We need to at least reduce the number of structures mentioned.

1045:), and as subject-based tables of contents linked to topics in the encyclopedia. The hierarchy is maintained through the use of heading levels and indented bullets. See 1016:

operations seems more natural to me, but I won't fight for it. If that is the only change that makes you feel uncomfortable, please validate the rest and undo this one.

83:, a type of article that presents a list of articles or sub-topics related to its subject in a hierarchical form. For the standardized set of outlines on Knowledge, see 588: 602:

ought to be doing: unlike the other "List of ..." articles, this page is much more than a bare list of links, and contains some useful expository prose. (The page

722:

outline is too technical, too overly detailed, and completely misorganized for helping one learn about algebraic structures. I propose the following changes:

674:

An algebraic structure consists of one or more sets, called underlying sets or carriers or sorts, closed under one or more operations, satisfying some axioms.

603: 565: 623: 384:

I would prefer a richer categorization suggested by Jipsen's webpage: varieties, quasivarieties, first order, etc.132.181.160.42 03:48, 19 July 2006 (UTC)

174:

If a structure has its own Wiki entry, it should be mentioned in this list. This does not preclude including structures for which there is no entry (yet);

1108: 123: 209:

The axioms are all identities among these five operations. The field structure dictates what these identities look like, but they're still identities.

944:

I think the outline article, however, should probably have longer lists and no detail on individual points, so as to function as a "sitemap" as the

318:

I would be fine with combining them, as long as there remains a clear visual distinction between the two: perhaps colored flags for the entries?

1113: 584: 481:

reason for including it in this list. Good thing, because group theory texts I've been browsing of late reveal a zoo well-stocked with species!

1103: 746:

Graphs are borderline algebraic, and WP:Math is discussing whether or not they really belong. Same can be said for sets with no operations.

850:

way back, but I am looking for ways to reintroduce some deleted terms. That said, the excessive detail on each entry simply cannot return.

662:

If we accept this definition, the neither the field of rational numbers nor the class of all fields would be an algebraic structure.

592: 460:. Now, before I go further, just to make sure we're on the same page: would you want to include "Alternating group" in this article? 1084: 372:

varieties", which already deals with such non-operations as norms, inner products, and gradings. Melchoir 03:55, 19 July 2006 (UTC)

910: 577: 599: 91: 58: 410:

It's the sole link at the bottom of the entry! Go ahead and merge in "Allowing additional structure" in any way you see fit.

159:

Burris and Sanka are very weak on modules, vector spaces, and algebras. Much of the structure you changed I inherited from

607: 573: 33: 641:

Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

552:

Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.

1050: 85: 941:. They are currently acting as examples, which typically appear in math articles as lists along with a little detail. 888:

they probably both need to keep existing (unmerged). I will be happy to take action to distinguish the two articles.

583:

There has recently been a lot of discussion regarding pages named "List of ..." or "Outline of ...": see for example

1023: 784: 331:

I would prefer a richer categorization suggested by Jipsen's webpage: varieties, quasivarieties, first order, etc.

883:. They were largely identical until recently. As you can see, I was involved earlier in a significant rewrite of 835: 245:

for two reasons. First, it was misplaced: the category of free modules (over some ring) is not a variety, and

1019: 831: 686:

An algebraic structure consists of one or two sets closed under some operations, functions, and relations

1080: 964: 657:

In universal algebra, a branch of pure mathematics, an algebraic structure is a variety or quasivariety.

246: 39: 783:

As can be seen I have greatly reduced the content. It has not been totally deleted, it still exists in

1072: 278: 227: 160: 765:

It's been an entire month, so I'm going to move ahead with changes along the lines described above.

938: 919: 906: 884: 879: 666: 525: 511: 332: 190: 182: 367:

I have had nothing to do with the content of "Allowing additional structure"; that's 100% legacy.

1046: 997: 953: 945: 893: 858: 817: 789: 770: 755: 619: 482: 433: 303:

varieties", which already deals with such non-operations as norms, inner products, and gradings.

291:

I have had nothing to do with the content of "Allowing additional structure"; that's 100% legacy.

98: 80: 506:

primitive. I was inspired to do this by the section "Symbolic Systems" on p. 1172 of Wolfram's

1088: 1055: 1027: 1001: 957: 923: 897: 862: 839: 821: 774: 759: 711: 528: 514: 485: 477: 473: 464: 436: 352: 335: 322: 307: 258: 231: 193: 1076: 707: 992:

Sorry to slow down your groove... I hope we can reinstate several parts of your edit soon.

610:

goes well beyond such annotations.) Therefore I think that renaming this page to include

1042: 1038: 915: 562: 186: 1097: 993: 949: 889: 854: 813: 766: 751: 615: 461: 349: 319: 304: 255: 737:

A subsection devoted to universal algebra (the abstract study of algebraic objects).

189:. It's more than a vector space over the reals and deserves a pigeonhole, but where? 1065: 632: 543: 703: 426: 422: 251: 73: 52: 585:

Wikipedia_talk:WikiProject_Mathematics#Undiscussed_List_-.3E_Outline_moves

443:

but the actual definition of an alternating group requires you to pick an

593:

Knowledge:Village_pump_(proposals)#RfC:_Elimination_of_outline_articles

1069:

doesn't have to have a operation within. Is that why is not incuded?

1061:"Group action" is missing, it fits well into "module like" structures. 878:

Do not under any circumstances put any material from the outline into

682:

I also do not understand what the editor meant with this sentence:

510:, but I may be misreading the work of Wolfram and his collaborators. 980:

For sure, I wish the changes to the references could be reproduced.

847: 695:

What is the intended difference between "function" and "relation"?

606:

links to some examples of "annotated lists". The information in

395:

I haven't seen it. Got a link? Melchoir 03:56, 19 July 2006 (UTC)

750:

I'll avoid editing this page for a week to wait for feedback.

15: 679:(Although I do not agree with the emphasis on the axioms.) 589:

Knowledge:Administrators' noticeboard/Incidents#Gamewizard71

425:, which fit the bill. Knowledge does include an entry named 95:, a collaborative effort to improve outlines on Knowledge. 937:

I don't think we should complately remove the lists from

542:

The following discussion is an archived discussion of a

447:, and once you do so, you're left with a unique object: 242: 97:

For guidance on building and maintaining outlines, see

631:

The above discussion is preserved as an archive of a

598:

I see this particular page as a good model for what

698:What does it mean to be "closed under a relation"? 614:in the title would set a constructive precedent. 652:I do not think that this sentence is correct: 456:. So "alternating group" is just the name of a 8: 604:Knowledge:Manual of Style/Stand-alone lists 363:The fate of "Allowing additional structure" 1070: 47: 21: 19: 909:has large flat lists of topics, whereas 226:The multilinear algebras, legacies from 1033:Quick explanation of Knowledge outlines 976:the least controversial things first. 717:Recommendations to improve this outline 49: 792:the two main purposes of outlines are: 170:Two objectives I have set for myself: 7: 930: 557:The result of the move request was: 181:Too bad you are not an authority on 89:. Outlines are within the scope of 665:I do agree with the terminology in 38:It is of interest to the following 1049:for a more in-depth explanation. 14: 1109:High-importance Outlines articles 905:: Agreed. I did notice that that 931: 534:Requested move "List ..." -: --> 72: 51: 20: 911:Outline of algebraic structures 578:Outline of algebraic structures 348:I haven't seen it. Got a link? 128:This article has been rated as 624:_"Outline_..."": --> 600:Knowledge:WikiProject Outlines 567:19:18, 14 September 2011 (UTC) 566:_"Outline_..."": --> 520:Matroids, antimatroids: where? 108:Knowledge:WikiProject Outlines 1: 1114:WikiProject Outlines articles 1028:14:22, 13 February 2013 (UTC) 1002:14:18, 12 February 2013 (UTC) 625:02:57, 6 September 2011 (UTC) 515:01:46, 7 September 2007 (UTC) 476:reveals that it is a type of 282:the living authority thereon. 111:Template:WikiProject Outlines 1104:List-Class Outlines articles 712:11:06, 24 October 2011 (UTC) 608:List of algebraic structures 574:List of algebraic structures 529:03:48, 23 October 2007 (UTC) 238:modules justice elsewhere. 86:Knowledge:Contents/Outlines 1130: 1056:00:02, 9 August 2015 (UTC) 958:18:14, 13 April 2012 (UTC) 929:That's OK, welcome to WP! 924:13:58, 13 April 2012 (UTC) 898:13:33, 13 April 2012 (UTC) 863:21:41, 28 April 2012 (UTC) 840:18:08, 27 April 2012 (UTC) 822:20:23, 13 April 2012 (UTC) 775:13:42, 13 April 2012 (UTC) 760:14:12, 12 March 2012 (UTC) 903:Response to Strong oppose 486:11:04, 30 July 2006 (UTC) 465:19:38, 25 July 2006 (UTC) 437:11:08, 25 July 2006 (UTC) 353:03:56, 19 July 2006 (UTC) 336:03:48, 19 July 2006 (UTC) 323:07:13, 18 July 2006 (UTC) 308:03:55, 19 July 2006 (UTC) 259:03:50, 19 July 2006 (UTC) 194:04:17, 18 July 2006 (UTC) 127: 67: 46: 1089:18:56, 31 May 2017 (UTC) 638:Please do not modify it. 549:Please do not modify it. 28:This article is rated 965:User:JP.Martin-Flatin 508:A New Kind of Science 247:Algebra (ring theory) 241:Yes, I deleted it in 279:Algebraic structures 228:Algebraic structures 161:Algebraic structures 92:WikiProject Outlines 939:algebraic structure 907:Algebraic structure 885:algebraic structure 880:Algebraic structure 667:Algebraic structure 494:Combinatory algebra 254:article, isn't it? 183:multilinear algebra 79:This article is an 1047:Knowledge:Outlines 206:over a given field 99:Knowledge:Outlines 34:content assessment 1091: 1075:comment added by 1052:The Transhumanist 478:permutation group 474:Alternating group 232:Hermann Grassmann 148: 147: 144: 143: 140: 139: 114:Outlines articles 1121: 1020:Jp.martin-flatin 936: 935: 934: 640: 551: 458:list of examples 134:importance scale 116: 115: 112: 109: 106: 76: 69: 68: 63: 55: 48: 31: 25: 24: 23: 16: 1129: 1128: 1124: 1123: 1122: 1120: 1119: 1118: 1094: 1093: 1063: 1035: 968: 932: 871: 719: 650: 648:"Is a variety"? 645: 636: 561:per request. - 547: 537: 522: 496: 455: 365: 153: 151:Opening heading 130:High-importance 113: 110: 107: 104: 103: 62:High‑importance 61: 32:on Knowledge's 29: 12: 11: 5: 1127: 1125: 1117: 1116: 1111: 1106: 1096: 1095: 1062: 1059: 1043:tree structure 1034: 1031: 990: 989: 985: 981: 967: 962: 961: 960: 942: 870: 869:Merge proposal 867: 866: 865: 851: 832:JacquesCarette 827: 826: 825: 824: 806: 805: 801: 796: 795: 794: 793: 778: 777: 748: 747: 744: 741: 738: 735: 732: 728: 718: 715: 700: 699: 696: 693: 688: 687: 677: 676: 660: 659: 649: 646: 644: 643: 633:requested move 572: 570: 555: 554: 544:requested move 538: 536: 532: 526:132.181.160.42 521: 518: 512:132.181.160.42 495: 492: 491: 490: 489: 488: 468: 467: 451: 418: 417: 416: 415: 414: 413: 412: 411: 401: 400: 399: 398: 397: 396: 388: 387: 386: 385: 379: 378: 374: 373: 364: 361: 360: 359: 358: 357: 356: 355: 341: 340: 339: 338: 333:132.181.160.42 326: 325: 315: 314: 313: 312: 311: 310: 295: 294: 293: 292: 286: 285: 284: 283: 272: 271: 266: 265: 264: 263: 262: 261: 235: 224: 217: 216: 211: 210: 191:132.181.160.42 187:linear algebra 179: 178: 175: 152: 149: 146: 145: 142: 141: 138: 137: 126: 120: 119: 117: 77: 65: 64: 56: 44: 43: 37: 26: 13: 10: 9: 6: 4: 3: 2: 1126: 1115: 1112: 1110: 1107: 1105: 1102: 1101: 1099: 1092: 1090: 1086: 1082: 1078: 1074: 1067: 1060: 1058: 1057: 1054: 1053: 1048: 1044: 1040: 1032: 1030: 1029: 1025: 1021: 1017: 1013: 1009: 1008: 1004: 1003: 999: 995: 986: 982: 979: 978: 977: 973: 972: 971:Edit Rejected 966: 963: 959: 955: 951: 947: 943: 940: 928: 927: 926: 925: 921: 917: 912: 908: 904: 900: 899: 895: 891: 886: 882: 881: 875: 874:Strong oppose 868: 864: 860: 856: 852: 849: 844: 843: 842: 841: 837: 833: 823: 819: 815: 810: 809: 808: 807: 802: 798: 797: 791: 786: 782: 781: 780: 779: 776: 772: 768: 764: 763: 762: 761: 757: 753: 745: 742: 739: 736: 733: 729: 725: 724: 723: 716: 714: 713: 709: 705: 697: 694: 690: 689: 685: 684: 683: 680: 675: 672: 671: 670: 668: 663: 658: 655: 654: 653: 647: 642: 639: 634: 629: 628: 627: 626: 621: 617: 613: 609: 605: 601: 596: 594: 590: 586: 581: 579: 575: 569: 568: 564: 560: 553: 550: 545: 540: 539: 535:"Outline ..." 533: 531: 530: 527: 519: 517: 516: 513: 509: 505: 501: 493: 487: 484: 483:202.36.179.65 479: 475: 472: 471: 470: 469: 466: 463: 459: 454: 450: 446: 441: 440: 439: 438: 435: 434:202.36.179.65 430: 428: 424: 409: 408: 407: 406: 405: 404: 403: 402: 394: 393: 392: 391: 390: 389: 383: 382: 381: 380: 376: 375: 370: 369: 368: 362: 354: 351: 347: 346: 345: 344: 343: 342: 337: 334: 330: 329: 328: 327: 324: 321: 317: 316: 309: 306: 301: 300: 299: 298: 297: 296: 290: 289: 288: 287: 280: 276: 275: 274: 273: 268: 267: 260: 257: 253: 248: 244: 240: 239: 236: 233: 229: 225: 223:determinants. 221: 220: 219: 218: 213: 212: 207: 202: 198: 197: 196: 195: 192: 188: 184: 176: 173: 172: 171: 168: 164: 162: 157: 150: 135: 131: 125: 122: 121: 118: 102: 100: 94: 93: 88: 87: 82: 78: 75: 71: 70: 66: 60: 57: 54: 50: 45: 41: 35: 27: 18: 17: 1071:— Preceding 1066:Group action 1064: 1051: 1036: 1018: 1014: 1010: 1006: 1005: 991: 974: 970: 969: 902: 901: 877: 873: 872: 828: 749: 720: 701: 681: 678: 673: 664: 661: 656: 651: 637: 630: 611: 597: 582: 571: 558: 556: 548: 541: 523: 507: 503: 499: 497: 457: 452: 448: 444: 431: 427:free modules 423:free modules 419: 366: 205: 200: 180: 169: 165: 158: 154: 129: 96: 90: 84: 40:WikiProjects 1077:Santropedro 946:WP:outlines 790:WP:outlines 252:Free module 1098:Categories 559:page moved 30:List-class 916:Yangjerng 563:GTBacchus 270:anything. 243:this edit 167:revised. 1085:contribs 1073:unsigned 994:Rschwieb 950:Rschwieb 890:Rschwieb 855:Rschwieb 814:Rschwieb 800:subject. 767:Rschwieb 752:Rschwieb 616:Jowa fan 462:Melchoir 350:Melchoir 320:Melchoir 305:Melchoir 256:Melchoir 215:algebra. 105:Outlines 59:Outlines 1039:Outline 984:though. 785:storage 727:stuff). 612:outline 132:on the 81:outline 1007:Answer 731:intro. 704:Aleph4 692:sorts? 421:found 199:Well, 36:scale. 988:once. 848:kudzu 1081:talk 1024:talk 998:talk 954:talk 920:talk 894:talk 859:talk 836:talk 818:talk 771:talk 756:talk 708:talk 620:talk 591:and 587:and 502:and 124:High 804:it. 788:at 669:: 635:. 201:all 1100:: 1087:) 1083:• 1026:) 1000:) 956:) 922:) 896:) 876:: 861:) 838:) 820:) 773:) 758:) 710:) 702:-- 622:) 595:. 580:– 576:→ 546:. 1079:( 1037:" 1022:( 996:( 952:( 918:( 892:( 857:( 834:( 816:( 769:( 754:( 706:( 618:( 504:K 500:S 453:n 449:A 445:n 234:. 136:. 101:. 42::

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.

Index