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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
Cross section of group extension      95
Curve, algebraic      271 307
CYCLE      60 464
Cylinder, mapping      470
dc.c      See descending chain condition
Decomposition, subdirect      575 578
Dedekind domain      293 295—297 413—414 497
Dedekind, R.      104 155 273 290 539
Degree of element      162
Degree of field extension      160
Degree of group representation      380
Degree of monomial      127
Degree of polynomial      121 127
Degree, residual class      254 254—257
Degree, separability      170
Degree, transcendence      184 311
Derivative      123
Destination      583
Determinant      526 527
diag      591
Diagram      590
Diagram, commutative      591
Diagram, constant      592
Dimension of algebraic variety      309 312
Dimension of group representation      380
Dimension of vector space      336
Dimension, global      510 511 510—514
Dimension, injective      509
Dimension, Krull      305 306 310
Dimension, projective      509 507—510
Direct limit      424 423—429 433
Direct limit of complexes      470
Direct limit of exact sequences      428
Direct limit of modules      424 427 447 451 453 455 497
Direct limit of sets      424 425
Direct limit of universal algebras      573 624
Direct product of bimodules      423
Direct product of Boolean lattices      557
Direct product of complexes      470
Direct product of groups      43 48 43—49 592
Direct product of homomorphisms      325
Direct product of injective modules      404
Direct product of modules      325 328 420 491 592
Direct product of projective modules      403
Direct product of rings      364—366 375
Direct product of universal algebras      568
Direct sum of complexes      470
Direct sum of group representations      380
Direct sum of groups      44 49
Direct sum of homomorphisms      326
Direct sum of injective modules      407
Direct sum of modules      325 325—329 402 421 429 433 446 451 491 494 495 508 594
Direct sum of projective modules      402
Direct sum, external      325
Direct sum, internal      327
Dirichlet, G.      188 214
Dirichlet’s Theorem      214
Discriminant      179 179—181 206
Distributivity      105 315 548 567
Division, polynomial      121 149
Divisor, greatest common      135 136 142
Domain      116 115—119 582 630.
Domain of binary relation      631
Domain, integral      116
Domain, integrally closed      283 284 287 295 296
Domain, normal      283
Domain, valuation      See valuation ring
Doohickey      416
Duality principle      540 541 543 546 549 553 585
Duplication of cube      226
Dyck, W.      27 31 33
Dyck’s theorem      33
EDGE      583
Eigenspace      345
Eigenvalue      345
Eilenberg, S.      401 403 463 500 613
Eisenstein, G.      144
Eisenstein’s Criterion      144 145 262
Element      See also elements
Element, algebraic      161 162 280
Element, cancellative      578
Element, central      382 516
Element, greatest      627 543
Element, idempotent      370
Element, identity      See identity element
Element, integral      279 280 281
Element, irreducible      134 142 550
Element, least      629 543
Element, left quasiregular      377
Element, maximal      625 111 145
Element, minimal      627
Element, nilpotent      112 376 377 577
Element, prime      134 142
Element, primitive      161
Element, purely inseparable      174
Element, quasiregular      377
Element, radical      218
Element, representative      133
Element, separable      171
Element, torsion      339
Element, torsion-free      339
Element, transcendental      161
Element, unique maximal      627
Element, zero      See zero element
Elementary linear transformation      77
Elementary matrix      77
Elements      See also element
Elements, algebraically dependent      182
Elements, algebraically independent      182
Elements, associate      133
Endomorphism of abelian group      106
Endomorphism of group      20
Endomorphism of module      320
Endomorphism of vector space      106
Endomorphism, nilpotent      51
Endomorphism, normal      50
Endomorphism, projection      52
Envelope, injective      See hull injective
Epimorphism      19 107 584
Epimorphism of modules      320 393
Epimorphism, split      395 402
Equalizer      593 595
Equipotence      640
Equivalence of categories      588 609
Equivalence of group extensions      95 98
Erlanger Programme      1
Euclid      138
Evaluation of polynomials      122 128
Evaluation of rational fractions      124 129
Exchange property      50 182 335
expansion      286 287
Exponentiation of cardinals      642 644
Ext      490
Extension of absolute values      247—261
Extension of fields      See field extension
Extension of groups      See group extension
Extension of rings      See ring extension
Extension of valuations      256—261
Extension, essential      409 408—410
Factor of normal series      71 348
Factor set      96
Factor, simple      74
Factorization theorem for algebras      517
Factorization theorem for groups      23
Factorization theorem for modules      322
Factorization theorem for rings      114
Factorization theorem for universal algebras      562
Family, algebraically dependent      182
Family, algebraically independent      182
Family, directed      15 423 425 568
Family, linearly independent      330
Feit and Thompson theorem      83
Feit, W.      83
Fermat prime      229
Field      116 155—268 569.
Field extension      159 159—230 530—534
Field extension, algebraic      164 164—230
Field extension, conjugate      194 199
Field extension, cyclic      219 218—220
Field extension, finite      160 164 297
Field extension, finitely generated      161
Field extension, Galois      197 197—225 297—300
Field extension, infinite      160
Field extension, infinite Galois      200—204
Field extension, linearly disjoint      185 186 532
Field extension, normal      192 191—197 199 225
Field extension, purely inseparable      173 172—175 192
Field extension, purely transcendental      181
Field extension, quadratic      283
Field extension, radical      221
Field extension, separable      171 169—172 189 184—190 195 532
Field extension, simple      161 162 170
Field extension, solvable by radicals      221 221—225
Field extension, totally transcendental      181
Field extension, transcendental      164 181—190
Field of fractions      118 119 285
Field of rational fractions      124 128 531
Field, algebraically closed      166
Field, Archimedean      232 233
Field, complete      243 249 259 264
Field, cyclotomic      212
Field, finite      192—193
Field, fixed      198 202
Field, formally real      234 234—239
Field, Galois      193
Field, ordered      231 231—239
Field, perfect      196 197 237 238
Field, quotient      See field of fractions
Field, real closed      235 235—239
Field, residue class      258 258—261
Field, skew      334
Field, splitting      191 192 191—193
Filter      462
Filtration on module      456 456—458
Filtration on ring      266 266—272
Filtration, $\mathfrak{a}$-      456
Filtration, $\mathfrak{a}$-adic      266 456
Filtration, $\mathfrak{a}$-stable      457 458
Five lemma      394
Fixed point      60
FRACTION      118 285.
Fraction, partial      139
Fraction, polynomial free      139
Fraction, reduced      139
Fractional ideal      290 291
Fractional ideal, finitely generated      291
Fractional ideal, invertible      291 413
Free product of groups      40 37—42 594
Free product of groups with amalgamation      41 42 584 595
Freyd, P.      609
Frobenius, G.      45 515 538
Frobenius’s Theorem      538
Func      587
Function, choice      628
Function, class      387 582
Function, coordinate      106 310
Function, Euler’s      46—47 207
Function, polynomial      311
Function, rational      129 311 314
functor      416 586 586—590
Functor, $\bigotimes$      437 438 445—448 607
Functor, additive      417 603
Functor, adjoint      606 604—612
Functor, colimit      599 606
Functor, completion      459 460
Functor, contravariant      416 588
Functor, covariant      416 586
Functor, derived      478—487
Functor, direct limit      427—429
Functor, dual      448
Functor, exact      419 420
Functor, Ext      488—493 507
Functor, forgetful      586 596 604 607 611 621 622
Functor, free group      586 604
Functor, free module      605 613
Functor, hom      417 418—423 589 597 599
Functor, homology      464
Functor, identity      587
Functor, inverse limit      432—434
Functor, left adjoint      606 622
Functor, left derived      479 479—484 486
Functor, left exact      419
Functor, limit      598 599 606
Functor, representable      612
Functor, right adjoint      606
Functor, right derived      484 485 486
Functor, right exact      445
Functor, Tor      493 493—496
Functor, tripleable      616 616—621 623
Fundamental theorem of algebra      137
Fundamental Theorem of Finitely Generated Abelian Groups      44 339
Fundamental Theorem of Galois Theory      198 203
g.l.b      See greatest lower bound
Galois connection      200 544 545
Galois group      197 204 197—225 224 299—300
Galois group of extension of $\mathbb{Q}$      214
Galois group of polynomial      204 204—211
Galois, E.      1 191 192
Garibaldi, S.      viii
Gauss integer      109
Gauss, G.      105 137 142 229 262
Gauss’s Lemma      143 262
GCD      135
Geometry, algebraic      271 273 275 276 307—314
GL      76
Goedel, K.      628
Going up      282
Gorenstein, D.      74
Graph      583
Graph, directed      583
Graph, discrete      592
Graph, finite      598
Graph, square      583
Graph, triangle      583
Grassmann, H.      523
Grell, H.      285
Grillet, P.A.      579
Grillet’s theorem      579
Groebner basis of ideal      150 148—154
Groebner basis of module      352 350—358
Groebner, W.      148
Group      8 1—104.
Group action      See group action
Group action, left      54 55
Group action, right      54
Group action, trivial      501
Group cohomology      100 464 468 500—507
Group extension      95 95—104
Group extension, equivalent      95 98
Group extension, split      99
Group generator      33
Group homology      463 464
Group of automorphisms      20 55
Group of finite length      49
Group of homomorphisms      415—423
Group of isometries      9
Group of rotations and symmetries      9
Group, alternating      36 60 74
Group, amalgam      41
Group, classical      76—83
1 2 3 4 5
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