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Grillet P.A. — Abstract Algebra
Grillet P.A. — Abstract Algebra

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Название: Abstract Algebra

Автор: Grillet P.A.

Аннотация:

About the first edition:
"The text is geared to the needs of the beginning graduate student, covering with complete, well-written proofs the usual major branches of groups, rings, fields, and modules...[n]one of the material one expects in a book like this is missing, and the level of detail is appropriate for its intended audience." (Alberto Delgado, MathSciNet)
"This text promotes the conceptual understanding of algebra as a whole, and that with great methodological mastery. Although the presentation is predominantly abstract...it nevertheless features a careful selection of important examples, together with a remarkably detailed and strategically skillful elaboration of the more sophisticated, abstract theories." (Werner Kleinert, Zentralblatt)
For the new edition, the author has completely rewritten the text, reorganized many of the sections, and even cut or shortened material which is no longer essential. He has added a chapter on Ext and Tor, as well as a bit of topology.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-nd edition

Год издания: 2007

Количество страниц: 669

Добавлена в каталог: 01.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$2^X$      539 540 549 553 554
$A_n$      36
$End_R$      332
$End_{\mathbb{Z}}$      316
$Irr (\alpha : K )$      162
$K^{1/p^{\infty}}$      173
$M_5$, a lattice      546 549
$M_n$, 1      332
$N_5$, a lattice      546
$R((X_i )_{I \in I}), R(X_1 , ..., X_n )$      128 129
$R[(X_i )_{I \in I} ], R[X_1 , ..., X_n ]$      126
$R^1$      108
$S^{-1}R$      285
$S_n$      58
$\aleph$, aleph      641
$\aleph_0$      641
$\bigotimes$      434 436
$\hat{Q}_p$      245
$\hat{\mathbb{Z}}_p$      245
$\mathbb{H}$, quaternion algebra      36 37
$\mathbb{N}$      1
$\mathbb{Q}$      1
$\mathbb{R}$      1
$\mathbb{Z}$      1 14 110
$\mathbb{Z}_n$      21 114 116 441
$\mathbb{Z}_{p^{\infty}}$      406 425
$\mathfrak{S}_k$      176
$\omega$, ordinal number      634
$^{op}$, opposite      317 540 585 627
$_R$Mods      583
$_RR$      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, $\mathfrak{a}$-adic      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
1 2 3 4 5
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