A first course in noncommutative rings:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2001
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Graduate texts in mathematics
131 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIX, 385 S. |
| ISBN: | 0387951830 0387953256 |
Internformat
MARC
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| 100 | 1 | |a Lam, Tsit-Yuen |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A first course in noncommutative rings |c T. Y. Lam |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 2001 | |
| 300 | |a XIX, 385 S. | ||
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| 490 | 1 | |a Graduate texts in mathematics |v 131 | |
| 650 | 4 | |a Anneaux non commutatifs | |
| 650 | 7 | |a Anéis e álgebras associativos |2 larpcal | |
| 650 | 7 | |a Niet-commutatieve structuren |2 gtt | |
| 650 | 7 | |a Ringen (wiskunde) |2 gtt | |
| 650 | 4 | |a Noncommutative rings | |
| 650 | 0 | 7 | |a Ringtheorie |0 (DE-588)4126571-3 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804136145193271296 |
|---|---|
| adam_text | Contents
Preface to the Second Edition vii
Preface to the First Edition ix
Notes to the Reader xvn
Chapter 1
Wedderburn Artin Theory 1
§1. Basic Terminology and Examples 2
Exercises for §1 22
§2. Semisimplicity 25
Exercises for §2 29
§3. Structure of Semisimple Rings 30
Exercises for §3 45
Chapter 2
Jacobson Radical Theory 48
§4. The Jacobson Radical 50
Exercises for §4 63
§5. Jacobson Radical Under Change of Rings 67
Exercises for §5 77
§6. Group Rings and the 7 Semisimplicity Problem 78
Exercises for §6 98
Chapter 3
Introduction to Representation Theory 101
§7. Modules over Finite Dimensional Algebras 102
Exercises for §7 116
xiii
xiv Contents
§8. Representations of Groups 117
Exercises for §8 137
§9. Linear Groups 141
Exercises for §9 152
Chapter 4
Prime and Primitive Rings 153
§10. The Prime Radical; Prime and Semiprime Rings 154
Exercises for §10 168
§11. Structure of Primitive Rings; the Density Theorem 171
Exercises for §11 188
§12. Subdirect Products and Commutativity Theorems 191
Exercises for §12 198
Chapter 5
Introduction to Division Rings 202
§13. Division Rings 203
Exercises for §13 214
§14. Some Classical Constructions 216
Exercises for §14 235
§15. Tensor Products and Maximal Subfields 238
Exercises for §15 247
§16. Polynomials over Division Rings 248
Exercises for §16 258
Chapter 6
Ordered Structures in Rings 261
§17. Orderings and Preorderings in Rings 262
Exercises for §17 269
§18. Ordered Division Rings 270
Exercises for §18 276
Chapter 7
Local Rings, Semilocal Rings, and Idempotents 279
§19. Local Rings 279
Exercises for §19 293
§20. Semilocal Rings 296
Appendix: Endomorphism Rings of Uniserial Modules 302
Exercises for §20 306
§21. Th Theory of Idempotents 308
Exercises for §21 322
§22. Central Idempotents and Block Decompositions 326
Exercises for §22 333
Contents xv
Chapter 8
Perfect and Semiperfect Rings 335
§23. Perfect and Semiperfect Rings 336
Exercises for §23 346
§24. Homological Characterizations of Perfect and Semiperfect Rings 347
Exercises for §24 358
§25. Principal Indecomposables and Basic Rings 359
Exercises for §25 368
References 370
Name Index 373
Subject Index 377
|
| adam_txt |
Contents
Preface to the Second Edition vii
Preface to the First Edition ix
Notes to the Reader xvn
Chapter 1
Wedderburn Artin Theory 1
§1. Basic Terminology and Examples 2
Exercises for §1 22
§2. Semisimplicity 25
Exercises for §2 29
§3. Structure of Semisimple Rings 30
Exercises for §3 45
Chapter 2
Jacobson Radical Theory 48
§4. The Jacobson Radical 50
Exercises for §4 63
§5. Jacobson Radical Under Change of Rings 67
Exercises for §5 77
§6. Group Rings and the 7 Semisimplicity Problem 78
Exercises for §6 98
Chapter 3
Introduction to Representation Theory 101
§7. Modules over Finite Dimensional Algebras 102
Exercises for §7 116
xiii
xiv Contents
§8. Representations of Groups 117
Exercises for §8 137
§9. Linear Groups 141
Exercises for §9 152
Chapter 4
Prime and Primitive Rings 153
§10. The Prime Radical; Prime and Semiprime Rings 154
Exercises for §10 168
§11. Structure of Primitive Rings; the Density Theorem 171
Exercises for §11 188
§12. Subdirect Products and Commutativity Theorems 191
Exercises for §12 198
Chapter 5
Introduction to Division Rings 202
§13. Division Rings 203
Exercises for §13 214
§14. Some Classical Constructions 216
Exercises for §14 235
§15. Tensor Products and Maximal Subfields 238
Exercises for §15 247
§16. Polynomials over Division Rings 248
Exercises for §16 258
Chapter 6
Ordered Structures in Rings 261
§17. Orderings and Preorderings in Rings 262
Exercises for §17 269
§18. Ordered Division Rings 270
Exercises for §18 276
Chapter 7
Local Rings, Semilocal Rings, and Idempotents 279
§19. Local Rings 279
Exercises for §19 293
§20. Semilocal Rings 296
Appendix: Endomorphism Rings of Uniserial Modules 302
Exercises for §20 306
§21. Th Theory of Idempotents 308
Exercises for §21 322
§22. Central Idempotents and Block Decompositions 326
Exercises for §22 333
Contents xv
Chapter 8
Perfect and Semiperfect Rings 335
§23. Perfect and Semiperfect Rings 336
Exercises for §23 346
§24. Homological Characterizations of Perfect and Semiperfect Rings 347
Exercises for §24 358
§25. Principal Indecomposables and Basic Rings 359
Exercises for §25 368
References 370
Name Index 373
Subject Index 377 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T16:19:51Z |
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| institution | BVB |
| isbn | 0387951830 0387953256 |
| language | English |
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| physical | XIX, 385 S. |
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| publisher | Springer |
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| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Lam, Tsit-Yuen Verfasser aut A first course in noncommutative rings T. Y. Lam 2. ed. New York [u.a.] Springer 2001 XIX, 385 S. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 131 Anneaux non commutatifs Anéis e álgebras associativos larpcal Niet-commutatieve structuren gtt Ringen (wiskunde) gtt Noncommutative rings Ringtheorie (DE-588)4126571-3 gnd rswk-swf Nichtkommutativer Ring (DE-588)4246997-1 gnd rswk-swf Nichtkommutativer Ring (DE-588)4246997-1 s DE-604 Ringtheorie (DE-588)4126571-3 s 1\p DE-604 Graduate texts in mathematics 131 (DE-604)BV000000067 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015385225&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lam, Tsit-Yuen A first course in noncommutative rings Graduate texts in mathematics Anneaux non commutatifs Anéis e álgebras associativos larpcal Niet-commutatieve structuren gtt Ringen (wiskunde) gtt Noncommutative rings Ringtheorie (DE-588)4126571-3 gnd Nichtkommutativer Ring (DE-588)4246997-1 gnd |
| subject_GND | (DE-588)4126571-3 (DE-588)4246997-1 |
| title | A first course in noncommutative rings |
| title_auth | A first course in noncommutative rings |
| title_exact_search | A first course in noncommutative rings |
| title_exact_search_txtP | A first course in noncommutative rings |
| title_full | A first course in noncommutative rings T. Y. Lam |
| title_fullStr | A first course in noncommutative rings T. Y. Lam |
| title_full_unstemmed | A first course in noncommutative rings T. Y. Lam |
| title_short | A first course in noncommutative rings |
| title_sort | a first course in noncommutative rings |
| topic | Anneaux non commutatifs Anéis e álgebras associativos larpcal Niet-commutatieve structuren gtt Ringen (wiskunde) gtt Noncommutative rings Ringtheorie (DE-588)4126571-3 gnd Nichtkommutativer Ring (DE-588)4246997-1 gnd |
| topic_facet | Anneaux non commutatifs Anéis e álgebras associativos Niet-commutatieve structuren Ringen (wiskunde) Noncommutative rings Ringtheorie Nichtkommutativer Ring |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015385225&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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