Passman D.S. — The algebraic structure of group rings :: Электронная библиотека попечительского совета мехмата МГУ

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Passman D.S. — The algebraic structure of group rings

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Название: The algebraic structure of group rings

Автор: Passman D.S.

Аннотация:

Group rings are easily defined, rather attractive algebraic objects. As the name implies, their study is a meeting place for two essentially different disciplines, the methods and results being a blending of group theory and ring theory. This book offers a comprehensive, self-contained treatment of group rings of infinite groups. The reprint edition contains an appendix which describes some recent developments in the field.

Язык:

Рубрика: Математика/

Статус предметного указателя: Указатель в процессе заполнения

ed2k: ed2k stats

Год издания: 1978

Количество страниц: 734

Добавлена в каталог: 24.11.2013

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Предметный указатель

$Con_{G}$       393
$D_{G} (\mathfrak{A})$       323
$\alpha^{G}$ -free module      540 543
$\Delta (G)$ (f.c. center)      115
$\Delta (G)$ (f.c. center) and primeness      129
$\Delta (G)$ (f.c. center) and primitivity      355 356 377
$\Delta (G)$ (f.c. center) and semiprimeness      131
$\Delta (G)$ (f.c. center), reduction to      122 124 127 128
$\Delta (G)$ (f.c. center), torsion subgroup of      117
$\delta G$       360 361
$\Delta^{+} (G)$       117
$\Delta^{+} (G)$ and annihilator ideals      143 144
$\Delta^{+} (G)$ and primitivity      353
$\Delta^{+} (G)$ , reduction to      142 143
$\Delta^{p} (G)$       308 309 311
$\Delta_{k} (G)$       182 186
$\mathfrak{A}$ -prime ring      365 367
$\mathscr{A} (K)$       684 685
$\mathscr{A} (K, F)$       695
Abelian groups and isomorphism questions      645 675 681 686 693
Abelian groups and semisimplicity      283
Abelian groups as products of cyclics      689
Abelian groups as quotient groups      134 135 282
Abelian groups, divisible subgroups of      19 676
Abelian groups, K-complete      131 132
Abelian groups, pure subgroups of      385 688
Abelian groups, Ulm invariants of      677 681
Abelian-by-finite groups      247 249
Abelian-by-finite groups and finite dimensional modules      539 573 574
Abelian-by-finite groups and polynomial identities      176 179 196 197 243 249
Abelian-by-finite groups and zero divisors      4 605 616
Abelian-by-finite groups as linear groups      531 536 537
Absolute field      386 539
Absolute value      33 35
Adjan, S.I.      416
Algebraic algebra      52 53
Algebraic algebra of bounded degree      173 216 217
Algebraic element      48 50
Algebraic group ring      53 54 55
Algebraically closed group      391 393
Amitsur, S.A.      168 169 175 176 209 251 252 264 268 271 273 280 283 290 291
Analytic group ring, $L^{1} (G)$ and $L^{2} (G)$       63 268
Analytic group ring, B (G)      63
Analytic group ring, U (G) and W (G)      64
Annihilator (l, i)      67 68 108
Annihilator free ideal      339 343 516 517 523
Annihilator free ideal and faithfulness      519
Annihilator ideal      140 143 144
Antiautomorphisms      5 33 59
Artin — Rees lemma      486 487 495
Artin — Rees property      485—500
Artin — Rees property, strong      485 487 488 552
Artin — Rees property, weak      486 492 493 496
Artin, E.      487
Artinian group ring      405 409 410 418
Augmentation ideal $\omega (K [G])$       67—109 405—468
Augmentation ideal $\omega (K [G])$ and AR properties      496 497
Augmentation ideal $\omega (K [G])$ , annihilators of      68
Augmentation ideal $\omega (K [G])$ , equal to Jacobson radical      314 415 416
Augmentation ideal $\omega (K [G])$ , filtrations of      84—105
Augmentation ideal $\omega (K [G])$ , generators of      67 86
Augmentation ideal $\omega (K [G])$ , intersection of powers      484
Augmentation ideal $\omega (K [G])$ , nilpotent      70
Augmentation ideal $\omega (K [G])$ , unique ideal      387 388 393 396
Baer's criterion      74 75
Baer, R.      74 333
Basis of filtration      87 89 95 99
Bass, H.      406 407
Bateman, J.M.      697
Bergman, G.M.      253 254 328 380 381 383 385 386 501 503 526 537 551
Berman, S.D.      664 675 681 684 686 687 693 694
Bonvallet, K.      388
Bounded representation degree      223—267
Bounded representation degree, r.b.n      224
Bourbaki, N.      287
Bovdi, A.A.      136 137 592
Brauer homomorphism      138
Brauer — Jennings — Zassenhaus $\mathscr{M}$ -series      481 483 670
Brauer, R.      58 138 140 537
Brown — McCoy radical $(\mathscr{B} R)$       352
Brown, K.A.      582 616 643
Burns, R.G.      136 638
Burnside problems      410 411 414 416
Burnside, W.      417
Center      113—167
Center and annihilator ideals      143 144 166
Center and primeness      129
Center and semiprimeness      130 131
Center of classical ring of quotients      153 154
Center of maximal ring of quotients      162
Center of simple summands      652
Center, basis of      113
Center, Brauer homomorphism of      138
Center, Jacobson radical of      119 120
Central idempotent, defect group of      140
Central idempotent, primitive      230 231 647 650 653
Central idempotent, support of      136 139
Central polynomial      202—214
Central trace map A/W      124 125 126
Centrally generated ideal      486 487 488
Chalabi, A.      313
CHARACTER      234 649 650
Character, orthogonality relations      651
Class sum      113 650
Classical ring of quotients      146—154

Classical ring of quotients and maximal ring of quotients      158
Classical ring of quotients of Goldie rings      456
Classical ring of quotients of prime P.I. algebras      212 213
Classical ring of quotients, center of      153 154
Clifford, A.H.      228 230 231 281
Cofinal ideals      366 367
Cohen, J.M.      638
Cohn, P.M.      250 582 608 609 611 612
Commutator, collection process      475 477 479
Commutator, n-fold      475
Commutator, subspace [A, A]      45 46
Commutator, triple      471
Compactness Theorem      245 246 247
Complex group algebra      33
Connell, I.G.      47 69 78 129 405
Contragredient module      59
Controller subgroup $\mathscr{C} (I)$       304—315
Controller subgroup $\mathscr{C} (I)$ of $\mathscr{P} K [G]$       346
Controller subgroup $\mathscr{C} (I)$ of NK [G]      309
Controlling subgroup      8 9 278 282 304
Core of subgroup      234
Crossed product      526
Dade, E.C.      660 661 669
Dark, R.      479
Defect group      140
Degree of module      224
Dennis, R.K.      696
Dense ideal      155
Deskins, E.      670
Diagonal equivalence      14 19 20 21
Dietzmann, A.P.      118
Dimension subgroups $D_{n} (K [G])$       85 469—485
Dimension subgroups $D_{n} (K [G])$ in characteristic 0      102 474
Dimension subgroups $D_{n} (K [G])$ in characteristic p      90 483 484
Dimension subgroups $D_{n} (K [G])$ , intersection of      484
Directed system of subgroups      292
Divisible group      19 676
Division ring embedding      601
Divisor set      427
Dyment, Z.Z.      327 333 346
E (G)      363
Essential extension      106
Essential submodule      452
Euler characteristic      630 631 632 635 636
Extension theorem for places      41
Faithful ideal      519 520
Farkas, D.R.      79 83 106 557 573 574 582 617 628 630 636
Feit, W.      537
Field extensions      273—291
Field extensions and Jacobson radical      280 283
Field extensions and N * K [G]      321
Field extensions and R-projectivity      275
Fields of first kind      684 690 693
Fields of second kind      684 686
Filtrations      84
Filtrations in characteristic 0      92—105 109
Filtrations in characteristic p      84—92 108
Finite conjugate group (f.c. group)      113—120
Finite endomorphism dimension      556—574
Finitely presented groups      553
Fisher, J.L.      696
Fisher, J.W.      364 367
Formanek, E.      51 52 54 162 167 199 200 203 207 212 220 295 353 364 367 373 376 377 398 582 615 633
Free groups      435 598
Free product and primitivity      373 376
Free product and zero divisors      612
Free product of groups      372 595
Free product of O-groups      597
Frobenius density theorem      44
Frobenius, G.      261 262
Fuchs, L.      592
G      55
G-prime ideal      342 517 519 523
G-semiprime ideal      342 517 519 523
Gabriel, P.      492
Generalized intersection theorem      336 340 341
Generalized polynomial identity      201 202
Gentile, E.R.      78
Glauberman, G.      664
Global dimension      433
Global dimension and localization      451
Global dimension of group extensions      437 442
Global dimension of group rings      434 435 450
Goldie ring      451—461
Goldie, A.W.      213 451 454 456 493 526
Golod, E.S.      411 413 414
Goursaud, j.m.      83 409 574
Graded module      621
Graded ring      621
Grothendieck, A.      626 627
Group ring      1 2
Hale, V.W.D.      638
Hall — Petresco formulas      477
Hall, M.      202 203
Hall, P.      92 101 102 393 395 421 425 472 474 477 478 525 537 539 543 544 545 556 577
Hampton, C.R.      332
Hartley, B.      388 484 557 573 574
Height, in N-sequence      86 95
Height, in Ulm series      677 678 688
Herstein, I.N.      53 268 273 611
Higman, D.G.      274
Higman, G.      588 656 698
Hilbert basis theorem      423
Hill, E.T.      108
Hirsch number h (G)      379 426
Homological dimension (h.d.)      430—451

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