"Highly recommended" by the Bulletin of the London Mathematical Society, this comprehensive, self-contained treatment of group rings was written by an authority on the subject. Suitable for graduate students, it was hailed by the Bulletin of the American Mathematical Society as "a majestic account… encyclopedic and lucid."1985 edition.
Author(s): Donald S. Passman
Year: 1978
Language: English
Pages: 726
Contents......Page 7
Part 1 Introduction......Page 12
1 Definitions......Page 13
2 Twisted Group Rings......Page 23
3 Tensor Products......Page 31
Exercises......Page 38
1 Complex Idempotents......Page 41
2 Places......Page 49
3 The Power Map......Page 55
4 Finite Groups......Page 65
Exercises......Page 73
1 Augmentation Annihilators......Page 77
2 Injective Modules......Page 84
3 Filtrations in Characteristic p......Page 94
4 Filtrations in Characteristic 0......Page 102
Exercises......Page 115
Part 2 Linear Identities......Page 120
1 Finite Conjugate Groups......Page 121
2 The Basic Reductions......Page 128
3 Idempotents and Annihilators......Page 139
4 The Classical Ring of Quotients......Page 154
5 The Maximal Ring of Quotients......Page 163
Exercises......Page 171
1 Standard Identities......Page 176
2 Subsets of Finite Index......Page 188
3 Primitive P.I. Algebras......Page 199
4 Central Polynomials......Page 210
Exercises......Page 222
1 Large Centralizers......Page 231
2 Finite Groups with r.b. n......Page 242
3 Semiprime P.I. Algebras......Page 253
4 Matrix Embedding......Page 258
Exercises......Page 270
1 Nondenumerable Fields......Page 276
2 Finite Extensions......Page 281
3 Abelian Extensions and Separable Algebras......Page 290
4 Semisimple Rings......Page 299
Exercises......Page 307
1 The Controller Subgroup......Page 312
2 The N^*-radical......Page 323
3 A Conjecture......Page 330
4 Radical Ideals and Intersection Theorems......Page 341
Exercises......Page 356
1 Extensions and the Center......Page 361
2 Some Basic Constructions......Page 372
3 Normal Abelian Subgroups......Page 386
4 Simple Augmentation Ideals......Page 395
Exercises......Page 404
Part 3 Finiteness Properties......Page 410
1 Artinian Rings......Page 411
2 Noetherian Rings......Page 425
3 Homological Dimension......Page 436
4 Goldie Rings......Page 457
Exercises......Page 467
1 Dimension Subgroups......Page 475
2 The Artin-Rees Property......Page 491
3 Hypercentral Rings......Page 506
4 Ideal Correspondence......Page 522
Exercises......Page 530
1 Solvable and Finite Linear Groups......Page 535
2 Philip Hall's Problem......Page 543
3 Some Residually Finite Groups......Page 551
4 Finite Endomorphism Dimension......Page 562
Exercises......Page 581
1 Unique Product Groups......Page 588
2 Ordered Groups......Page 598
3 Supersolvable Groups......Page 611
4 Polycyclic-by-finite Groups......Page 622
Exercises......Page 643
1 Central Subfields......Page 650
2 Finite Metabelian Groups......Page 666
3 Infinite Abelian Groups......Page 681
4 Fields of the First Kind......Page 694
Exercises......Page 703
References......Page 709
Index......Page 719
