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Grillet P.A. — Abstract Algebra
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Название: Abstract AlgebraАвтор: Grillet P.A. Аннотация: About the first edition:
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 2-nd editionГод издания: 2007Количество страниц: 669Добавлена в каталог: 01.06.2008Операции: Положить на полку |
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539 540 549 553 554 36 332 316 162 173 546 549 332 546 128 129 126 108 285 58 641 641 434 436 245 245 36 37 1 1 1 1 14 110 21 114 116 441 406 425 176 634 317 540 585 627 583 315 a.c.c See ascending chain condition Abel, N. 1 191 224 Abelian group 11 44—46 99 315 405—408 456 492 493 495 576 Abelian group, divisible 406—408 Abelian group, free 330 Abelian group, subdirectly irreducible 576 Abelian group, torsion-free 452 Abelian group, totally ordered 251 Abel’s theorem 224 abs 583. See also Pecs Absolute value 239 239—266 Absolute value, Archimedean 240 241 Absolute value, equivalent 240 Absolute value, extension of 247—261 Absolute value, nonarchimedean 241 Absolute value, p-adic 241 Absolute value, trivial 239 action See also group action Action by automorphisms 92 Action by inner automorphisms 56 Action by left multiplication 54 Action by permutations 54 Action in group extension 96 Action set 96 Action, trivial 501 Addition 2 Adjoint functor theorem 610 609—612 Adjunction 606 607 608 610 613 al-Kwowarizmi vii 188 Algebra vii 311 381 515 515—538. Algebra, Artinian 534 Algebra, associative 515 Algebra, boolean See Boolean lattice Algebra, central 535 Algebra, central simple 535—536 Algebra, commutative 273 Algebra, division 534 537 538 Algebra, exterior 524 523—527 530 Algebra, free 518 520 Algebra, graded 517 Algebra, group 382 381—386 502 Algebra, homological 463 463—514 Algebra, nonassociative 515 Algebra, quotient 516 517 Algebra, simple 534 534—538 Algebra, symmetric 521 521—524 530 Algebra, T - 614 Algebra, tensor 519 518—520 530 Algebra, universal 559—580 Algebraic set 275 276 304 307 307—310 Algebraic set, affine 307 Algebraic set, irreducible 309 Algebraic set, projective 307 Almost all 107 Alphabet 6 Amalgam of groups 41 ANN 317 323 324 Annihilator of element 324 Annihilator of ideal 545 Annihilator of module 317 Arity 559 arrow 582 583 Artin — Rees lemma 457 Artin — Schreier theorem 236 Artin — Wedderburn theorem 367 370 Artin, E. vii 37 105 155 191 198 220 228 231 236 359 Associativity 3 566 Associativity, adjoint 444 atom 555 Automorphism of group 20 Automorphism, inner 56 Axiom of Choice 628 628—631 Baer, R. 403 Baer’s Criterion 404 Base, transcendence See transcendence base Basis See also Groebner basis Basis of ideal 146 Basis of module 330 Basis of vector space 335 Basis, dual 448 Bass, H. 407 Beck, J. 616 618 Beck’s theorem 618 Belkhouche, B. vii Bidule 8 Bifunctor 588 589 Bihomomorphism of bimodules 438 Bihomomorphism of modules 435 Bimodule 417 529 Bimodule of homomorphisms 418 Bims 588 Binomial theorem 107 Biproduct 601 600 Birkhoff, G. vii 539 549 552 555 558 570 574 576 Birkhoff’s theorem 549; 552 577; Boole, R. 552 Bound, greatest lower 539 Bound, least upper 540 Bound, lower 539 Bound, upper 628 540 Boundary 463 464 Buchberger, B. 148 Buchberger’s Algorithm 152 354 Buchberger’s Criterion 151 352 Burnside, W. 1 372 380 Burnside’s Theorem 372; 391 Butterfly lemma 72 Cancellation laws 10 12 116 Cantor, G. 639 641 Cantor-Bernstein theorem 640 Card 642 Cardano, G. 191 206 207 cardinal number 640 639—644 Cardinal number, finite 640 Cardinal number, infinite 640 Cardinality 641 Cartan, H. 401 403 463 Cartesian product 43 324 592 Cartesian product of categories 588 Cartesian product of classes 582 Cartesian product, empty 2 Category 582 582—624 Category of Abelian groups 583 600 602 616 620 Category of bimodules 588 600 602 Category of groups 583 584 596 598 599 611 617 620 Category of left R-modules 583 596 598 599 600 601 602 617 620 Category of partially ordered sets 616 Category of paths 584 Category of R -algebras 584 596 Category of rings 584 585 586 596 617 620 Category of sets 583 596 598 599 609 616 Category of T -algebras 615 Category, abelian 602 602—604 Category, additive 600 600—604 Category, cocomplete 598 Category, comma 611 Category, complete 596 595—599 Category, dual 585 Category, equivalent 588 590 Category, free 584 Category, functor 587 600 604 Category, isomorphic 588 Category, locally small 589 Category, of topological spaces 617 620 Category, opposite 584 585 588 593 598 600 Category, small 583 Category, tripleable 616 616—621 623 Cats 87 Cauchy, A. 1 Cauchy’s Theorem 64 Cayley — Hamilton theorem 345 Cayley’s Theorem 54 Center of algebra 535 Center of GL(V ) 78 Center of group 56 Center of p -group 57 Center of SL(V ) 78 centralizer 56 537 545 Centralizer of permutation 63 Chain 626 15 111 463 464 628 Chain condition, ascending 626 146 296 346 Chain condition, descending 627 300 347 Chain of subsets 15 Chain, maximal 547 553 Chain, singular 463 CHARACTER 386 386—392 Character of group 386 Character of group representation 386 Character, complex 389 389—392 Character, irreducible 386 Character, one-dimensional 387 Character, regular 387 Character, trivial 387 Characteristic of domain 116 Characteristic of field 116 156 Characteristic of ring 115 Chase, S. 407 Chinese remainder theorem 289 class 581 582 631 Class equation 57 Class, associate 133 Class, cohomology 468 Class, conjugacy 56 65 384 Class, homology 464 Class, proper 581 Class, small 582 Classification Theorem 74 Clifford, A.H. 5 Clifford’s theorem 386 Closure, algebraic 167 165—168 237 238 Closure, integral 283 Closure, real 236 Coboundary 463 467 468 501 Cochain 463 467 501 Cochain, singular 463 CoCone 594 Cocycle 468 501 Codimension 304 Codomain 582 Coefficient, leading 121 146 351 Coequalizer 595 Coequalizer, absolute 621 Coequalizer, split 617 Cohomology 464 Cohomology of groups 501 500—507 Cohomology, singular 464 Coimage 603 Coker 393 Cokernel 602 Cokernel of homomorphism 393 396 594 Colimit 593 594 Colimit, directed See direct limit Combination, infinite 316 Combination, linear 316 Commutativity 3 567 Commutator of two elements 83 Commutator series 84 Commutator subgroup 83 Comparison theorem 472 477 Complement 554 Completion of exact sequences 460 Completion of field 244 243—246 Completion of module 461 456—462 Completion of partially ordered set 544 Completion of ring 266 266—268 461 Completion, 266 301 458 Completion, MacNeille 545 Complex bar 503 Complex chain 463 464 Complex cochain 464 Complex, negative 464 Complex, positive 464 Complex, singular 463 464 Component, homogeneous 517 Component, simple 369 Composite of fields 158 159 164 185 composition 582 Concatenation 6 Cone 424 430 591 594 Cone, colimit 593 594 610 Cone, limit 424 430 592 610 Cone, mapping 470 Congruence 562 564 Congruence on a group 563 Congruence on a ring 564 Congruence on a semigroup 564 Congruence, fully invariant 572 Congruence, induced by ideal 577 Conjugate elements 36 56 194 216 Conjugate field extensions 194 Conjugate permutations 62 Conjugate subgroups 65 Connection, Galois See Galois connection Constructible 226 226—230 Construction by straightedge and compass 226 225—230 Construction, standard See triple Contraction 286 287 coordinates 310 330 Coproduct 594 595 Coset 16 15—17 Coset of normal subgroup 19 Coset, left 15 Coset, right 15 Cosyzygy 476 508 510 Cover 547 634 Create coequalizers 617 Create everything en:1:1 Create limits 599 612 616 624 Cross section 629
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, a lattice 
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, aleph 
, quaternion algebra 
, ordinal number 
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Mods 
-adic 
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