The Jacobson radical of classical rings:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Harlow, Essex
Longman Scientific & Technical
1991
|
| Edition: | 1. publ. |
| Series: | Pitman monographs and surveys in pure and applied mathematics
53 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 563 S. |
| ISBN: | 058205947X |
Staff View
MARC
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| 245 | 1 | 0 | |a The Jacobson radical of classical rings |c G. Karpilovsky |
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| 650 | 7 | |a radical |2 inriac | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Introduction ix
Notation xiii
Chapter 1. Preliminaries 1
1. Notation and terminology 1
2. Chain conditions 3
3. Semisimple modules 8
4. Direct decomposition of rings 10
5. Matrix rings 13
Chapter 2. Basic properties of J(R) 17
6. Definitions and elementary properties 17
7. The upper and lower nilradicals 25
8. Primitive rings 30
9. The Jacobson radical and idempotents 37
10. Nilpotency of J(R) 50
11. Conditions for nil ideals to be nilpotent 56
12. Essential nilpotency 61
13. The Jacobson radical of endomorphism rings 63
A. Semisimple modules 64
B. Fitting s theorem 65
C. Projective and injective modules 73
D. Modules of finite length 81
14. Normalizing extensions 82
Chapter 3. Algebras over fields 88
15. Tensor products of modules 88
16. Tensor product of algebras 94
17. Some general results on J{A®r B) 99
18. Field theoretic prerequisites 101
v
vi CONTENTS
19. Fundamental properties of J(A) 105
A. Conditions for J{A) to be nil 106
B. Basic properties of J(A ®f B) 110
C. Tensor products of fields 116
D. Separable algebras 117
20. Frobenius and symmetric algebras 124
A. General properties 124
B. Projective covers 130
C. Fundamental theorems 132
D. Representations and blocks 137
E. Kulshammer s theorem 144
21. Criteria for J(A) to be principal 149
Chapter 4. Graded rings 159
22. Monoid graded algebras 159
23. Examples 170
A. Monoid rings 170
B. Monoid crossed products 172
C. Skew monoid rings 177
D. Twisted monoid rings 179
24. Induced modules 182
25. The Jacobson radical and induced modules 195
26. The graded Jacobson radical 198
27. Strongly graded algebras 209
28. Graded group rings 215
29. Graded Maschke s theorem 220
30. Applications to the Jacobson radical 221
A. Finite groups 222
B. Group theoretic results 228
C. Infinite groups 232
31. Unique product groups and monoids 241
32. Algebras graded by t.u.p. monoids 247
33. The Jacobson radical of crossed products 256
A. Monoid crossed products 257
B. Applications to polynomial rings 271
C. Applications to skew polynomial rings 278
D. Group crossed products 281
E. An application 292
Chapter 5. Twisted group algebras 295
34. Semiprimitivity of FaG, G finite 295
35. Some group theoretic results 298
CONTENTS vii
36. Compatible actions 302
37. The nilpotent radical of FaG 307
38. Semiprimitivity of FaG, G arbitrary 314
39. Semiprimitivity and JF groups 320
40. Preparatory results for the metabelian case 326
41. Metabelian groups 331
Chapter 6. Infinite group algebras 336
42. Preliminary results 336
43. Commutative group algebras 346
44. Conditions for J(RG) = I(G) 350
45. Nil ideals 358
A. Nonzero nil ideals 358
B. Some auxiliary results 364
C. Nil ideals of bounded degree 367
46. Local nilpotence of J{FG) 373
A. Bounded automorphisms 373
B. Isolated subsets 378
C. Some technical lemmas 385
D. Local nilpotence 395
Chapter 7. The semiprimitivity problem 400
47. Prologue: known and unknown 400
48. The iV radical 405
A. Definitions and elementary properties 405
B. A characterization of N {FG) 406
C. Radical properties 412
D. Direct products 417
49. Linear groups 419
50. Locally finite groups 425
A. Assumed group theoretic facts 426
B. Preparatory results 429
C. Locally subnormal subgroups 439
D. A reductions 443
E. The main theorem 450
51. Locally solvable groups 455
Chapter 8. Finite group algebras 457
52. Elementary results 457
53. A description of J{FG) 464
A. The general case 464
B. The p solvable case 468
viii CONTENTS
54. Blocks and their defect groups 474
55. Morita s theorem 483
56. Criteria for J(FG) to be principal 487
57. Frobenius groups 492
58. The dimension of J(FG) 499
59. The Jacobson radical of Z(FG) 508
A. A description of J(Z{FG)) 508
B. The dimension of J{Z{FG)) 510
C. Criteria for J(FG) = FG ¦ J{Z(FG)) 523
Bibliography 527
Index 555
|
| any_adam_object | 1 |
| author | Karpilovsky, Gregory |
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| dewey-ones | 512 - Algebra |
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| dewey-search | 512/.4 |
| dewey-sort | 3512 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV004548898 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:14:09Z |
| institution | BVB |
| isbn | 058205947X |
| language | English |
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| physical | XVI, 563 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Longman Scientific & Technical |
| record_format | marc |
| series | Pitman monographs and surveys in pure and applied mathematics |
| series2 | Pitman monographs and surveys in pure and applied mathematics |
| spelling | Karpilovsky, Gregory Verfasser aut The Jacobson radical of classical rings G. Karpilovsky 1. publ. Harlow, Essex Longman Scientific & Technical 1991 XVI, 563 S. txt rdacontent n rdamedia nc rdacarrier Pitman monographs and surveys in pure and applied mathematics 53 Anneaux de semigroupes ram Anneaux gradués ram Jacobson, radicaux de ram anneau inriac radical inriac Graded rings Jacobson radical Semigroup rings Jacobson-Radikal (DE-588)4162648-5 gnd rswk-swf Halbgruppenring (DE-588)4158791-1 gnd rswk-swf Graduierter Ring (DE-588)4158003-5 gnd rswk-swf Jacobson-Radikal (DE-588)4162648-5 s Graduierter Ring (DE-588)4158003-5 s DE-604 Halbgruppenring (DE-588)4158791-1 s Pitman monographs and surveys in pure and applied mathematics 53 (DE-604)BV000022446 53 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002799029&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Karpilovsky, Gregory The Jacobson radical of classical rings Pitman monographs and surveys in pure and applied mathematics Anneaux de semigroupes ram Anneaux gradués ram Jacobson, radicaux de ram anneau inriac radical inriac Graded rings Jacobson radical Semigroup rings Jacobson-Radikal (DE-588)4162648-5 gnd Halbgruppenring (DE-588)4158791-1 gnd Graduierter Ring (DE-588)4158003-5 gnd |
| subject_GND | (DE-588)4162648-5 (DE-588)4158791-1 (DE-588)4158003-5 |
| title | The Jacobson radical of classical rings |
| title_auth | The Jacobson radical of classical rings |
| title_exact_search | The Jacobson radical of classical rings |
| title_full | The Jacobson radical of classical rings G. Karpilovsky |
| title_fullStr | The Jacobson radical of classical rings G. Karpilovsky |
| title_full_unstemmed | The Jacobson radical of classical rings G. Karpilovsky |
| title_short | The Jacobson radical of classical rings |
| title_sort | the jacobson radical of classical rings |
| topic | Anneaux de semigroupes ram Anneaux gradués ram Jacobson, radicaux de ram anneau inriac radical inriac Graded rings Jacobson radical Semigroup rings Jacobson-Radikal (DE-588)4162648-5 gnd Halbgruppenring (DE-588)4158791-1 gnd Graduierter Ring (DE-588)4158003-5 gnd |
| topic_facet | Anneaux de semigroupes Anneaux gradués Jacobson, radicaux de anneau radical Graded rings Jacobson radical Semigroup rings Jacobson-Radikal Halbgruppenring Graduierter Ring |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002799029&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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