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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
Product, of ideals      250 256 268
Projection      83 154 325 349 581
Projective module      585ff 590
Public Key Code      278
Purely inseparable      563
Purely transcendental      560
Quadratic extensions      434
Quadratic subfields of cyclic quartic fields, criterion      552
Quartic equations, formulas for roots      548ff
Quasidihedral group      71 87 101 188 493
Quasidihedral group as Galois group      493
Quaternion group      34 69 125
Quaternion group as Galois group      498
Quaternion group, generalized      180
Quaternion ring      226 230 231 237 257
Quintic, insolvability      542 552
Quotient field      261ff
Quotient group      73 76
Quotient module      325
Quotient ring      239ff
Quotient space      335
R-module      315
Radical      258 267
Radical extensions      538ff
Radical of ideal      289
Rank of a free module      316 330
Rank of a group      166 220
Rank of a module      371 379 380
Rank of linear transformation      340
Rational canonical form      383ff 386 387 388 393
Rational functions      265 428 443
Rational valued characters, criterion for      614
Reduced row echelon form      350
Reducible element      282
Reducible module      578 580
Reduction homomorphism      245
Regular character      602 633
Regular representation      121 575 579 585 599
Relations      26 220
Relations matrix      381
Relative degree, of a field extension      424
Relatively prime      4
Replacement Theorem, for vector spaces      337
Representation, linear      571
Representation, matrix      571
Representation, permutation      41
Representatives      9 75 77
Residue class      8
Resolvent cubic      529
Resolvent polynomials      529 537 548 552 556 557
Restricted direct product      158
Resultant      534ff
Right group actions      130
Ring      225
Ring of algebraic integers      628
Ring of fractions      261ff 281
Root, of polynomial      301
Roots of unity      23 451 464
Row equivalent      350
Row rank      345 359
Row reduced      350
Ruler and compass constructions      447
scalar      335
Scalar matrix      236
Scalar transformations      324
Schur’s lemma      333 584 585 593
Second Orthogonality Relation      608 615
Semidihedral group      see “Quasidihedral group”
Semidirect product      176ff
Semisimple      591
Separability, criterion for      459ff
Separable degree of a polynomial      463
Separable degree of field extension      563
Separable extension      463
Separable polynomial      458ff
Separating transcendence base      564 566
Sign, of permutation      108
Similar linear transformations      387
Similar matrices      346
Similar matrices, criterion      389
Similar representations      578
Simple extensions      429 505ff 508 509 512
Simple group      91 103
Simple groups, classification of      104 214
Simple module      578 591 593
Skew field      226
Smith normal form      391 414
Solution of cubic equations      543ff
Solution of quartic equations      548ff
Solvability of quintic, criterion      552
Solvable extensions      538ff 552
Solvable group      105 196ff 621 626 628
Solved by radicals      538 540 552
Solving linear equations      351
span      328 335 353
Special linear group      47
Specialization      562
Splitting field      425 448ff 455 486
Splitting field of $(x^2 - 2)(x^2 - 3)$      449
Splitting field of $x^2 + 1$      427
Splitting field of $x^2 + x + 1$ over $\mathbb{F}_2$      428
Splitting field of $x^2 - 2$      449
Splitting field of $x^2 - t$ over k(t)      428
Splitting field of $x^3 - 2$      449
Splitting field of $x^4 + 4$      449
Splitting field of $x^4 + px + p$      532
Splitting field of $x^4 - 2x^2 - 2$      496
Splitting field of $x^4 - px^2 + q$      532
Splitting field of $x^6 - 2x^3 - 2$      537 558
Splitting field of $x^8 - 2$      490
Splitting field of $x^n - 1$      451
Splitting field of $x^p - 2$      453
Splitting field of $x_p - x - a$ over $\mathbb{F}_p$      503
Sporadic simple group      104
Square root of a matrix      413
Squaring the Circle, impossibility of      446
Stabilizer      43 50 113
Stable subspace      319
Straightedge and compass constructions      443ff
Subgroup      23 45
Subgroup criterion      46
Subgroup, generators of      61
Subgroup, maximal      64
Subgroup, normal      82
Submodule      315
Submodule criterion      320
Subring      230
subspace      335
Sum of ideals      250
Sum of submodules      325
Surjective      2
Sylow subgroup      102 140 162
Sylow’s Theorem      93 140ff
Symmetric functions      361 523ff
Symmetric group      28
Table, group      22
Tchebotarov Density Theorem      556
Thompson subgroup      140
Thompson’s Theorem      198
Torsion element      321
Torsion free      371
Torsion module      332
Torsion subgroup      47
Torsion submodule      321 370
Trace ideal, of group ring      577
Trace of element in a field      497
Trace of matrix      247 356 533
Trace submodule      577
Transcendental extensions      558ff
Transitive      116
Transitive subgroup of $S_n$      521 554
Transitive subgroups of $S_5$      556
TRANSPOSE      359
Transposition      107
Trascendence base      559
Trascendence degree      559
Trascendental      432 559
Trisecting an angle using ruler      447
Trisecting an angle, impossibility of      446
Trivial representation      575
Twisted polynomial ring      297
U.F.D.      see “Unique Factorization Domain”
Unique factorization domain      282ff 294 299 300
Uniqueness of finite fields      462
Uniqueness of splitting field      455
UNITS      228 235 237 252
Units in $\mathbb{Z}/n\mathbb{Z}$      269 308
Universal property of free groups      217
Universal property of free modules      331
Universal side divisor      281
Upper central series      192
Upper triangular matrices      48
Valuation ring      232
Vandermonde determinant      534
Vector space      315 335ff
Viergruppe      68
Virtual character      638
Wedderburn components      591
Wedderburn decomposition      591
Wedderburn’s Theorem on Finite Division Rings      469
Wedderburn’s Theorem on Semisimple Rings      590
Weight, of monomial      536
Well denned      2
Well Ordering of $\mathbb{Z}$      4
Wilson’s Theorem      464
Word      217 218
Wreath product      189
Zariski closed set      260 261
Zariski topology      260 312
Zero divisors      228 233
Zorn’s Lemma      253 645ff
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