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Dummit D.S., Foote R.M. — Abstract Algebra
Dummit D.S., Foote R.M. — Abstract Algebra



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Название: Abstract Algebra

Авторы: Dummit D.S., Foote R.M.

Аннотация:

Widely acclaimed algebra text. This book is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics. The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in-depth results, using numerous examples and exercises to aid the reader's understanding. In this way, readers gain an appreciation for how mathematical structures and their interplay lead to powerful results and insights in a number of different settings


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 657

Добавлена в каталог: 08.11.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$Aut(\mathbb{R}/\mathbb{Q})$      480
$A_4$, characters of      618
$A_5$, simplicity of      129 151
$A_n$      110
$A_n$, conjugacy in      132
$A_n$, simplicity of      129 151ff
$D_{10}$, characters of      612 614
$D_{12}$, representation of      632
$D_{2n}$      24
$D_{2n}$, characters of      602 642
$D_{2n}$, commutator subgroup      172
$D_{2n}$, conjugacy in      133
$D_{2n}$, representations of      576 579
$End_R$ (M)      324 333 360
$GL_3(\mathbb{F}_2)$      209ff 213
$GL_n$      33 236 340 345
$Hom_F(V, W)$      343
$Hom_R(M, M)$      322
$QD_{2n}$      71 87 101 188 493
$Q_8$      34 69 125
$Q_8$, characters of      602 612 614 617
$Q_8$, representations of      576 584
$SL_n$      47 104
$S_3$, characters of      608 616 633
$S_3$, representations of      598
$S_4$, characters of      609 618
$S_5$, characters of      619
$S_n$      28
$S_n$ as Galois group      562
$S_n$, characters of      613
$S_n$, conjugacy in      126 ff 133
$S_n$, representations of      575 579 583 584 602
$S_p$, normalizer of Sylow p-subgroup      133 206
$S_p$, Sylow p-subgroups of      206
$S_{p^2}$, , Sylow p-subgroups of      189
$V_4$      68
$Z_n$      56
$\mathbb{C}$      427 530
$\mathbb{Z}$-modules      317 323 367
$\mathbb{Z}[\sqrt{D}]$      232 277ff 287 288
A.C.C.      see “Ascending chain condition”
Abelian extensions of $\mathbb{Q}$      510ff 514
Abelian group      18 159ff 317
Abelian group, Fundamental Theorem      159ff
Abelian group, representations of      584 585 597
Action group      40 113
Action group, left versus right      130
Affine algebraic set      312
Affine n-space      310 316
Affords, a representation      113 574
Algebra      572
Algebraic closure of finite field      502
Algebraic closures      455ff 502
Algebraic element      432 439
Algebraic extension      432 439
Algebraic integer      622ff
Algebraically closed      311 455 530
Algebraically conjugate characters      613ff
Algebraically independent      559
Algebraically indistinguishable      430
Algorithm for Jordan Canonical Form      408
Algorithm for rational canonical form      393
Alternating function      361
Alternating group      108ff 151ff
Angle, trisecting      446 447
Annihilated by      316
Annihilator, of submodule      371
Annihilators      248 321 360
ansition matrix      346
Artin — Schreier extensions      503 550
Ascending chain condition      288 369
Associate      282
Associative      17
Augmentation ideal      245 255 577
Augmentation map      245
Augmented matrix      349
Automorphism group      39 134ff
Automorphism group of a field      471
Automorphism group of a field extension      471
Automorphism group, $D_8$      137
Automorphism group, $Q_8$      137
Automorphism group, $S_8$      137
Automorphism group, cyclic group      136 137
Automorphism group, elementary abelian group      137 323
Automorphism, of a field      468 471
Base field      423
Basis      330 336
Berlekamp’s Factorization Algorithm      503ff
Betti number      159 374
Bijective      2
Binary operation      17
Binary relation      3
Binomial theorem      249
Biquadratic extensions      442 496 503
Biquadratic polynomial      532
Block      118
Boolean ring      231 248 257 270
Building-Up Lemma      338
Burnside’s $p^aq^b$ Theorem      198 621ff
Burnside’s Basis Theorem      201
Burnside’s Lemma      612
Cancellation laws      21
Cardano’s formulas for roots of a cubic      543ff 545
Cardinality      1
Cartesian product      1 643ff
Castelnuevo’s Theorem      560
Casus irreducibilis      547 551
Cauchy’s Theorem      92 95 102
Cayley — Hamilton theorem      390
Cayley’s Theorem      121
Center of group      49
Center of p-group      126 190
Center of ring      231 572 592 596
Central idempotent      333
Central product      158
Centralize      94
centralizer      48
Centralizer of representation      584
Change of basis      346
Character of a group      482 601
Character table      615
Characteristic of a field      422
Characteristic of a ring      249
Characteristic p fields      461
Characteristic polynomial      384
Characteristic subgroup      135 136 139
Chinese remainder theorem      267ff 270 307
Chinese Remainder Theorem for modules      333
Class equation      125
Class field theory      514
Class functions      601 605
Classical Greek Problems      446
Closed      17
Coefficient matrix      349
Cofactor      364
Column rank      345 359
Comaximal ideals      268 280
Commutative      17 18
Commutator      89 170 195ff
Commutator series      197
Commutator subgroup      89 170 195ff 583
Commute, diagram      101
Companion matrix      386
Complement, of subgroup      182 626
Completely reducible module      578 582 591
Composite extensions      505ff
Composites of fields      440ff
Composition factors      103
Composition series      103
Congruence class      8
Conjugacy class      124 597
Conjugate field elements      487
Conjugate of element      82 124
Conjugate of set      124
Conjugation      43 51
Conjugation in $A_n$      132
Conjugation in $S_n$      126ff 133
Constituent, of a module      578
Constructibility of the regular n-gon      515ff
Constructible elements      444
Construction of cube roots      447
Construction of the regular 17-gon      516 518ff
Corresponding group actions      130
Coset      77
Coset representatives      77
Cramer’s Rule      363
Cubic equations, formulas for roots      543ff 545
CYCLE      28
Cycle decomposition      28 116
Cycle decomposition algorithm      29
Cycle type      127
Cycle types, of automorphisms      543 553
Cyclic extensions      538 540
Cyclic group      53ff 160
Cyclic group, characters of      615 616
Cyclic group, representations of      575 579 584 599
Cyclic module      327 373
Cyclic subgroup      29
Cyclotomic extensions      464ff 510ff
Cyclotomic fields      451ff 464ff
Cyclotomic polynomial      304 401 465ff 468
Cyclotomy      512
D.C.C.      see “Descending chain condition”
Decomposable module      578
Dedekind and Hasse Criterion      281
Degree 1 representations      583 584 601 613
Degree of a field element      433
Degree of a field extension      424 433
Degree of polynomial      234 293
Degree of representation      571 597 603 624
Degree of symmetric group      28
Density of primes      556
Derivative, of a polynomial      306 458
Derived series      197
Descending chain condition      591
Determinant of a matrix      247 360 366
Diagonalizable matrices, criterion      405
Dihedral group      24
Dihedral group as Galois group      558
DIMENSION      335 338
Diophantine equations      245 276
Direct product      19 153ff 158 643
Direct product of modules      329 333 341
Direct product of rings      267
Direct sum      158
Direct sum of modules      329 333 334 341
Direct sum of rings      231
Dirichlet’s Theorem on Primes in Arithmetic Progression      469
Discrete valuation ring      233 260 272
Discriminant      524
Discriminant as resultant      536
Discriminant of $p^{th}$ cyclotomic polynomial      536
Discriminant of a cubic      527
Discriminant of a polynomial      524 533 536
Discriminant of a quadratic      526
Discriminant of a quartic      529
Distributive law      33 225
Divisible group      65 86 590
Division algorithm      5 271
Division ring      226 252 256
Double coset      118
Doubling the cube, impossibility of      446
Doubly transitive      118 613
Dual basis      357
Dual group      168
Dual vector space      357ff
Dual vector space, characters of      609 614 616 633
Dual vector space, representations of      583
Eigenspace      384
Eigenvalue      341 383
Eigenvector      341 383
Eisenstein’s Criterion      303 304
Elementary Abelian group      137 156 317
Elementary Divisor Decomposition Algorithm      407ff
Elementary divisors      162 375
Elementary Jordan matrix      404
Elementary row operations      350 390
Elementary symmetric functions      522
Elliptic function field      566
Embedding of fields      483 489
Endomorphism      324
Endomorphism ring      324
Equivalence class      3
Equivalence relation      3
Equivalent representations      578 602 604
Euclidean algorithm      5 271 274 294
Euclidean Domain      271 279 285 294
Euclidean Domains, modules over      381ff 401ff
Euler $\phi$-function      7 269 310
Euler’s theorem      96
Evaluation homomorphism      244 358
Even permutation      108
Exceptional characters      639
Existence of finite fields      462
EXPONENT      167
Exponentials of matrices      415
Expressed by radicals      540
Extension field      423
Extension theorem for isomorphisms of fields      431 454
External direct product      173
F-algebra      572
Factor group      76
Factor through, homomorphism      101
Faithful      42 113
Faithful representation      571 613
Feit — Thompson theorem      104 198 636
Fermat primes      515
Fermat’s Little Theorem      96
Fermat’s Theorem on sums of squares      309
FG-modules      574 580 582
Fiber      2 73
Field      33 226 252 254 422
Field generated by      429
Field of fractions      261ff 281
Finite dimensional      338
Finite extensions      433 434 439
Finite field, existence and uniqueness      462 499
Finite fields      499ff 503
Finitely generated      64 159 220 250 327 436 559 582
First Orthogonality Relation      607 615
Fix, an element      471
Fixed field      473 485
Formal Laurent series      238
Formal power series      238 257 289
Formally real fields      442
Fourier analysis      610
Fractional linear transformations      480 560
Frattini subgroup      201
Frattini’s Argument      195
Free Abelian group      159 223 332
Free generators      220
Free groups      216ff
Free module      316 330
Free nilpotent group      223
Free rank, of a module      374
Frobenius group      170 552 556 557 633
Frobenius group as Galois group      552 557 558
Frobenius group, characters of      633 641
Frobenius kernel      633
Frobenius map      461 468 469 479 499 518
1 2 3
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