Commutative group algebras:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Dekker
1983
|
| Edition: | 1. print. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 223 S. |
| ISBN: | 0824719182 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | Contents
PREFACE v
CHAPTER 1. PREREQUISITES 1
1. Notation and Terminology 1
2. Background Sketch 5
CHAPTER 2. PRELIMINARY RESULTS 27
1. Definitions 27
2. Elementary Properties 29
CHAPTER 3. RING THEORETIC PROPERTIES 44
1. Chain Conditions. Regular and Completely
Reducible Group Algebras 44
2. Characters, Direct Decompositions, and
Irreducible Modules 48
3. Idempotents 59
4. Nil and Jacobson Radicals 68
5. Krull Dimension 75
CHAPTER 4. INTEGRAL DOMAINS 83
1. GCD Domains 83
2. Unique Factorization Domains 90
3. Krull Domains 108
CHAPTER 5. STUDY OF UNITS US
1. Units of Finite Order 115
2. The Unit Group of Group Algebras of
Torsion Free Groups 120
3. Splitting Unit Groups 127
4. The Isomorphism Class of U(ZG) 136
5. The Unit Group of 2[en] 141
6. Effective Construction of Units of ZG 151
ix
x Contents
CHAPTER 6. ISOMORPHISM QUESTIONS 160
1. Preliminary Results 161
2. Finite Groups 166
3. May s Conjecture 174
4. Algebraically Closed Fields 182
5. Countable p Groups 185
6. Real Group Algebras 190
CHAPTER 7. RESEARCH PROBLEMS 198
REFERENCES 203
NOTATION 215
INDEX 219
|
| adam_txt |
Contents
PREFACE v
CHAPTER 1. PREREQUISITES 1
1. Notation and Terminology 1
2. Background Sketch 5
CHAPTER 2. PRELIMINARY RESULTS 27
1. Definitions 27
2. Elementary Properties 29
CHAPTER 3. RING THEORETIC PROPERTIES 44
1. Chain Conditions. Regular and Completely
Reducible Group Algebras 44
2. Characters, Direct Decompositions, and
Irreducible Modules 48
3. Idempotents 59
4. Nil and Jacobson Radicals 68
5. Krull Dimension 75
CHAPTER 4. INTEGRAL DOMAINS 83
1. GCD Domains 83
2. Unique Factorization Domains 90
3. Krull Domains 108
CHAPTER 5. STUDY OF UNITS US
1. Units of Finite Order 115
2. The Unit Group of Group Algebras of
Torsion Free Groups 120
3. Splitting Unit Groups 127
4. The Isomorphism Class of U(ZG) 136
5. The Unit Group of 2[en] 141
6. Effective Construction of Units of ZG 151
ix
x Contents
CHAPTER 6. ISOMORPHISM QUESTIONS 160
1. Preliminary Results 161
2. Finite Groups 166
3. May's Conjecture 174
4. Algebraically Closed Fields 182
5. Countable p Groups 185
6. Real Group Algebras 190
CHAPTER 7. RESEARCH PROBLEMS 198
REFERENCES 203
NOTATION 215
INDEX 219 |
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| indexdate | 2024-07-09T20:46:35Z |
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| isbn | 0824719182 |
| language | English |
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| physical | X, 223 S. |
| publishDate | 1983 |
| publishDateSearch | 1983 |
| publishDateSort | 1983 |
| publisher | Dekker |
| record_format | marc |
| spelling | Karpilovsky, Gregory Verfasser aut Commutative group algebras 1. print. New York [u.a.] Dekker 1983 X, 223 S. txt rdacontent n rdamedia nc rdacarrier Abelian groups Commutative algebra Group algebras Kommutativer Gruppenring (DE-588)4727872-9 gnd rswk-swf Kommutative Algebra (DE-588)4164821-3 gnd rswk-swf Abelsche Gruppe (DE-588)4140988-7 gnd rswk-swf Gruppenring (DE-588)4158469-7 gnd rswk-swf Kommutative Algebra (DE-588)4164821-3 s DE-604 Gruppenring (DE-588)4158469-7 s Abelsche Gruppe (DE-588)4140988-7 s 1\p DE-604 Kommutativer Gruppenring (DE-588)4727872-9 s 2\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015095486&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Karpilovsky, Gregory Commutative group algebras Abelian groups Commutative algebra Group algebras Kommutativer Gruppenring (DE-588)4727872-9 gnd Kommutative Algebra (DE-588)4164821-3 gnd Abelsche Gruppe (DE-588)4140988-7 gnd Gruppenring (DE-588)4158469-7 gnd |
| subject_GND | (DE-588)4727872-9 (DE-588)4164821-3 (DE-588)4140988-7 (DE-588)4158469-7 |
| title | Commutative group algebras |
| title_auth | Commutative group algebras |
| title_exact_search | Commutative group algebras |
| title_exact_search_txtP | Commutative group algebras |
| title_full | Commutative group algebras |
| title_fullStr | Commutative group algebras |
| title_full_unstemmed | Commutative group algebras |
| title_short | Commutative group algebras |
| title_sort | commutative group algebras |
| topic | Abelian groups Commutative algebra Group algebras Kommutativer Gruppenring (DE-588)4727872-9 gnd Kommutative Algebra (DE-588)4164821-3 gnd Abelsche Gruppe (DE-588)4140988-7 gnd Gruppenring (DE-588)4158469-7 gnd |
| topic_facet | Abelian groups Commutative algebra Group algebras Kommutativer Gruppenring Kommutative Algebra Abelsche Gruppe Gruppenring |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015095486&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT karpilovskygregory commutativegroupalgebras |