An introduction to group rings:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht ; Boston ; London
Kluwer Academic Publishers
[2002]
|
| Schriftenreihe: | Algebras and applications
1 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 351-363) and index |
| Beschreibung: | xi, 371 Seiten Illustrationen |
| ISBN: | 1402002386 1402002394 |
Internformat
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| 264 | 1 | |a Dordrecht ; Boston ; London |b Kluwer Academic Publishers |c [2002] | |
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| 300 | |a xi, 371 Seiten |b Illustrationen | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | Titel: An introduction to group rings
Autor: Milies, César Polcino
Jahr: 2002
An Introduction to Group Rings by .. César PolcinoMilies Instituto de Matemática e Estatistica, Universidade de Sao Paulo, Säo Paulo, Brasil and Sudarshan K. Sehgal department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Canada KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON
Contents Preface ix 1 Groups 1 1.1 Basic Concepts .......................... 1 1.2 Homomorphisms and Factor Groups.............. 10 1.3 Abelian Groups.......................... 18 1.4 Group Actions, p-groups and Sylow Subgroups ........ 21 1.5 Solvable and Nilpotent Groups................. 27 1.6 FC Groups ............................ 42 1.7 Free Groups and Free Products................. 46 1.8 Hamiltonian Groups................. 54 1.9 The Hirsch Number ....................... 59 2 Rings, Modules and Algebras 63 2.1 Rings and Ideals......................... 63 2.2 Modules and Algebras ...................... 76 2.3 Free Modules and Direct Sums................. 80 2.4 Finiteness Conditions ...................... 83 2.5 Semisimplicity .......................... 91 2.6 The Wedderbum-Artin Theorem................ 98 2.7 The Jacobson Radical ......................106 2.8 Rings of Algebraic Integers ...................113 2.9 Orders...............................115 2.10 Tensor Products .........................117 3 Group Rings 125 3.1 A Brief History ..........................125 3.2 Basic Facts............................129 3.3 Augmentation Ideals.......................134 v
Vi CONTENTS 3.4 Semisimplicity ..........................138 3.5 Abelian Group Algebras.....................144 3.6 Some Commutative Subalgebras ................150 4 A Glance at Group Representations 159 4.1 Definition and Examples.....................159 4.2 Representations and Modules..................170 5 Group Characters 179 5.1 Basic Facts............................179 5.2 Characters and Isomorphism Questions ............190 6 Ideals in Group Rings 199 6.1 Ring Theoretic Formulas.....................200 6.2 Nilpotent Ideals..........................205 6.3 Nilpotent Augmentation Ideals.................208 6.4 Semiprime Group Rings.....................209 6.5 Prime Group Rings........................212 6.6 Chain Conditions in AG.....................214 7 Algebraic Elements 219 7.1 Introduction............................219 7.2 Idempotent Elements.......................222 7.3 Torsion Units...........................224 7.4 Nilpotent Elements........................226 8 Units of Group Rings 233 8.1 Introduction............................233 8.2 Trivial Units ...........................241 8.3 Finite Groups...... 247 8.4 Units of ZS 3 ....... 254 8.5 Infinite Groups..........................263 8.6 Finite Generation of U{7,G) ...................271 8.7 Central Units...........................280 9 The Isomorphism Problem 287 9.1 Introduction............................287 9.2 The Normal Subgroup Correspondence.............291 9.3 Metabelian Groups........................292 9.4 Circle Groups...........................298 9.5 Further Results..........................306
CONTENTS vii 9.6 The Modular Isomorphism Problem..............308 10 Free Groups of Units 321 10.1 Free Groups............................321 10.2 Free Groups of Units.......................324 10.3 Explicit Free Groups.......................327 10.4 Explicit Free Groups in H....................331 11 Properties of the Unit Group 333 11.1 Integral Group Rings.......................333 11.2 Group Algebras..........................342 Bibliography 351 Index 364
|
| any_adam_object | 1 |
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| dewey-full | 512/.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.4 |
| dewey-search | 512/.4 |
| dewey-sort | 3512 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T19:03:01Z |
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| isbn | 1402002386 1402002394 |
| language | English |
| lccn | 2001050674 |
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| series | Algebras and applications |
| series2 | Algebras and applications |
| spelling | Milies, César Polcino 1944- (DE-588)1014758033 aut An introduction to group rings by César Polcino Milies: Instituto de Matematica e Estatistica, Universidade de Sāo Paulo, Sāo Paulo, Brasil ; Sudarshan K. Sehgal: Department of Mathematical and Statistical Sciences, University of Alberta, edmonton, canada Dordrecht ; Boston ; London Kluwer Academic Publishers [2002] © 2002 xi, 371 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Algebras and applications 1 Includes bibliographical references (p. 351-363) and index Group rings Gruppenring (DE-588)4158469-7 gnd rswk-swf Gruppenring (DE-588)4158469-7 s DE-604 Sehgal, Sudarshan K. 1936- (DE-588)172402239 aut Algebras and applications 1 (DE-604)BV035420975 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009879416&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Milies, César Polcino 1944- Sehgal, Sudarshan K. 1936- An introduction to group rings Algebras and applications Group rings Gruppenring (DE-588)4158469-7 gnd |
| subject_GND | (DE-588)4158469-7 |
| title | An introduction to group rings |
| title_auth | An introduction to group rings |
| title_exact_search | An introduction to group rings |
| title_full | An introduction to group rings by César Polcino Milies: Instituto de Matematica e Estatistica, Universidade de Sāo Paulo, Sāo Paulo, Brasil ; Sudarshan K. Sehgal: Department of Mathematical and Statistical Sciences, University of Alberta, edmonton, canada |
| title_fullStr | An introduction to group rings by César Polcino Milies: Instituto de Matematica e Estatistica, Universidade de Sāo Paulo, Sāo Paulo, Brasil ; Sudarshan K. Sehgal: Department of Mathematical and Statistical Sciences, University of Alberta, edmonton, canada |
| title_full_unstemmed | An introduction to group rings by César Polcino Milies: Instituto de Matematica e Estatistica, Universidade de Sāo Paulo, Sāo Paulo, Brasil ; Sudarshan K. Sehgal: Department of Mathematical and Statistical Sciences, University of Alberta, edmonton, canada |
| title_short | An introduction to group rings |
| title_sort | an introduction to group rings |
| topic | Group rings Gruppenring (DE-588)4158469-7 gnd |
| topic_facet | Group rings Gruppenring |
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