Introductory lectures on rings and modules:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
1999
|
| Edition: | 1. publ. |
| Series: | London Mathematical Society student texts
47 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 238 S. |
| ISBN: | 0521643406 0521644070 |
Staff View
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Record in the Search Index
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| adam_text | Contents
PREFACE vii
1 RINGS 1
1.1 Basic definitions and examples 2
1.2 Ring homomorphisms 20
1.3 Localization of integral domains 34
1.4 Unique factorization 43
1.5 * Additional noncommutative examples 50
2 MODULES 63
2.1 Basic definitions and examples 64
2.2 Direct sums and products 78
2.3 Semisimple modules 88
2.4 Chain conditions 97
2.5 Modules with finite length 102
2.6 Tensor products 109
2.7 Modules over principal ideal domains 121
2.8 *Modules over the Weyl algebras 127
3 STRUCTURE OF NONCOMMUTATIVE RINGS 137
3.1 Prime and primitive ideals 138
3.2 The Jacobson radical 147
3.3 Semisimple Artinian rings 155
3.4 *Orders in simple Artinian rings 161
4 REPRESENTATIONS OF FINITE GROUPS 171
4.1 Introduction to group representations 172
4.2 Introduction to group characters 187
4.3 Character tables and orthogonality relations 196
A APPENDIX 207
A.I Review of vector spaces 207
A.2 Zorn s lemma 211
A.3 Matrices over commutative rings 213
A.4 Eigenvalues and characteristic polynomials 216
A.5 Noncommutative quotient rings 221
A.6 The ring of algebraic integers 226
v
vi CONTENTS
BIBLIOGRAPHY 229
LIST OF SYMBOLS 231
INDEX 233
|
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| dewey-ones | 512 - Algebra |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
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| indexdate | 2024-07-09T18:43:20Z |
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| isbn | 0521643406 0521644070 |
| language | English |
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| physical | VIII, 238 S. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | London Mathematical Society student texts |
| series2 | London Mathematical Society student texts |
| spelling | Beachy, John A. Verfasser aut Introductory lectures on rings and modules John A. Beachy 1. publ. Cambridge Cambridge Univ. Press 1999 VIII, 238 S. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society student texts 47 Anneaux non commutatifs Anneaux non commutatifs ram Modules (Algèbre) Modules (algèbre) ram Noncommutative rings (Algebra) Modules (Algebra) Noncommutative rings Modul (DE-588)4129770-2 gnd rswk-swf Nichtkommutativer Ring (DE-588)4246997-1 gnd rswk-swf Nichtkommutativer Ring (DE-588)4246997-1 s Modul (DE-588)4129770-2 s DE-604 London Mathematical Society student texts 47 (DE-604)BV000841726 47 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009066355&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Beachy, John A. Introductory lectures on rings and modules London Mathematical Society student texts Anneaux non commutatifs Anneaux non commutatifs ram Modules (Algèbre) Modules (algèbre) ram Noncommutative rings (Algebra) Modules (Algebra) Noncommutative rings Modul (DE-588)4129770-2 gnd Nichtkommutativer Ring (DE-588)4246997-1 gnd |
| subject_GND | (DE-588)4129770-2 (DE-588)4246997-1 |
| title | Introductory lectures on rings and modules |
| title_auth | Introductory lectures on rings and modules |
| title_exact_search | Introductory lectures on rings and modules |
| title_full | Introductory lectures on rings and modules John A. Beachy |
| title_fullStr | Introductory lectures on rings and modules John A. Beachy |
| title_full_unstemmed | Introductory lectures on rings and modules John A. Beachy |
| title_short | Introductory lectures on rings and modules |
| title_sort | introductory lectures on rings and modules |
| topic | Anneaux non commutatifs Anneaux non commutatifs ram Modules (Algèbre) Modules (algèbre) ram Noncommutative rings (Algebra) Modules (Algebra) Noncommutative rings Modul (DE-588)4129770-2 gnd Nichtkommutativer Ring (DE-588)4246997-1 gnd |
| topic_facet | Anneaux non commutatifs Modules (Algèbre) Modules (algèbre) Noncommutative rings (Algebra) Modules (Algebra) Noncommutative rings Modul Nichtkommutativer Ring |
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