Alternative loop rings:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam [u.a.]
Elsevier
1996
|
| Schriftenreihe: | North-Holland mathematics studies
184 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 387 S. graph. Darst. |
| ISBN: | 0444824383 |
Internformat
MARC
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| 100 | 1 | |a Goodaire, Edgar G. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Alternative loop rings |c Edgar G. Goodaire ; Eric Jespers ; César Polcino Milies |
| 264 | 1 | |a Amsterdam [u.a.] |b Elsevier |c 1996 | |
| 300 | |a XV, 387 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a North-Holland mathematics studies |v 184 | |
| 650 | 7 | |a Algebra nao associativa |2 larpcal | |
| 650 | 7 | |a Anneaux de groupes |2 ram | |
| 650 | 4 | |a Alternative rings | |
| 650 | 4 | |a Group rings | |
| 650 | 4 | |a Loops (Group theory) | |
| 700 | 1 | |a Jespers, Eric |e Verfasser |4 aut | |
| 700 | 1 | |a Milies, César Polcino |d 1944- |e Verfasser |0 (DE-588)1014758033 |4 aut | |
| 830 | 0 | |a North-Holland mathematics studies |v 184 |w (DE-604)BV000003247 |9 184 | |
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Datensatz im Suchindex
| _version_ | 1804125932909232128 |
|---|---|
| adam_text | Contents
Preface ix
Introduction 1
Chapter I. Alternative Rings 5
1. Fundamentals 5
2. The real quaternions and the Cayley numbers 13
3. Generalized quaternion and Cayley Dickson algebras 15
4. Composition algebras 23
5. Tensor products 38
Chapter II. An Introduction to Loop Theory and to Moufang Loops 49
1. What is a loop? 49
2. Inverse property loops 60
3. Moufang loops 63
4. Hamiltonian loops 68
5. Examples of Moufang loops 80
Chapter III. Nonassociative Loop Rings 85
1. Loop rings 85
2. Alternative loop rings 90
3. The LC property 94
4. The nucleus and centre 100
5. The norm and trace 103
Chapter IV. RA Loops 107
1. Basic properties of RA loops 107
2. RA loops have LC 119
3. A description of an RA loop 122
xiii
xiv CONTENTS
Chapter V. The Classification of Finite RA Loops 125
1. Reduction to indecomposables 125
2. Finite indecomposable groups 131
3. Finite indecomposable RA loops 138
4. Finite RA loops of small order 143
Chapter VI. The Jacobson and Prime Radicals 147
1. Augmentation ideals 149
2. Radicals of abelian group rings 153
3. Radicals of loop rings 159
4. The structure of a semisimple alternative algebra 166
Chapter VII. Loop Algebras of Finite Indecomposable RA Loops 173
1. Primitive idempotents of
commutative rational group algebras 174
2. Rational loop algebras of finite RA loops 182
Chapter VIII. Units in Integral Loop Rings 195
1. Trivial torsion units 196
2. Bicyclic and Bass cyclic units 200
3. Trivial units 204
4. Trivial central units 212
5. Free subgroups 213
Chapter IX. Isomorphisms of Integral Alternative Loop Rings 223
1. The isomorphism theorem 225
2. Inner automorphisms of alternative algebras 228
3. Automorphisms of alternative loop algebras 233
4. Some conjectures of H. J. Zassenhaus 236
Chapter X. Isomorphisms of Commutative Group Algebras 247
1. Some results on tensor products of fields 248
2. Semisimple abelian group algebras 252
3. Modular group algebras of abelian groups 258
4. The equivalence problem 261
Chapter XI. Isomorphisms of Loop Algebras of Finite RA Loops 267
1. Semisimple loop algebras 267
CONTENTS XV
2. Rational loop algebras 271
3. The equivalence problem 282
Chapter XII. Loops of Units 289
1. Reduction to torsion loops 289
2. Group identities 294
3. The centre of the unit loop 309
4. Describing large subgroups 314
5. Examples 320
Chapter XIII. Idempotents and Finite Conjugacy 333
1. Central idempotents 333
2. Nilpotent elements 346
3. Finite conjugacy 348
Bibliography 369
Index 377
Notation 383
|
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| author | Goodaire, Edgar G. Jespers, Eric Milies, César Polcino 1944- |
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| author_facet | Goodaire, Edgar G. Jespers, Eric Milies, César Polcino 1944- |
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| dewey-ones | 512 - Algebra |
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| dewey-sort | 3512 14 |
| dewey-tens | 510 - Mathematics |
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| id | DE-604.BV011419323 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:09:25Z |
| institution | BVB |
| isbn | 0444824383 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007677273 |
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| physical | XV, 387 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Elsevier |
| record_format | marc |
| series | North-Holland mathematics studies |
| series2 | North-Holland mathematics studies |
| spelling | Goodaire, Edgar G. Verfasser aut Alternative loop rings Edgar G. Goodaire ; Eric Jespers ; César Polcino Milies Amsterdam [u.a.] Elsevier 1996 XV, 387 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier North-Holland mathematics studies 184 Algebra nao associativa larpcal Anneaux de groupes ram Alternative rings Group rings Loops (Group theory) Jespers, Eric Verfasser aut Milies, César Polcino 1944- Verfasser (DE-588)1014758033 aut North-Holland mathematics studies 184 (DE-604)BV000003247 184 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007677273&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Goodaire, Edgar G. Jespers, Eric Milies, César Polcino 1944- Alternative loop rings North-Holland mathematics studies Algebra nao associativa larpcal Anneaux de groupes ram Alternative rings Group rings Loops (Group theory) |
| title | Alternative loop rings |
| title_auth | Alternative loop rings |
| title_exact_search | Alternative loop rings |
| title_full | Alternative loop rings Edgar G. Goodaire ; Eric Jespers ; César Polcino Milies |
| title_fullStr | Alternative loop rings Edgar G. Goodaire ; Eric Jespers ; César Polcino Milies |
| title_full_unstemmed | Alternative loop rings Edgar G. Goodaire ; Eric Jespers ; César Polcino Milies |
| title_short | Alternative loop rings |
| title_sort | alternative loop rings |
| topic | Algebra nao associativa larpcal Anneaux de groupes ram Alternative rings Group rings Loops (Group theory) |
| topic_facet | Algebra nao associativa Anneaux de groupes Alternative rings Group rings Loops (Group theory) |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007677273&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003247 |
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