Introduction to ring theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London ; Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong
Springer
2000
|
| Schriftenreihe: | Springer undergraduate mathematics series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 229 S. graph. Darst. 24 cm |
| ISBN: | 1852332069 |
Internformat
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| 100 | 1 | |a Cohn, Paul M. |d 1924-2006 |e Verfasser |0 (DE-588)121230538 |4 aut | |
| 245 | 1 | 0 | |a Introduction to ring theory |c P. M. Cohn |
| 264 | 1 | |a London ; Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong |b Springer |c 2000 | |
| 300 | |a X, 229 S. |b graph. Darst. |c 24 cm | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer undergraduate mathematics series | |
| 650 | 4 | |a Anneaux (Algèbre) | |
| 650 | 7 | |a Ringen (wiskunde) |2 gtt | |
| 650 | 4 | |a Rings (Algebra) | |
| 650 | 0 | 7 | |a Ringtheorie |0 (DE-588)4126571-3 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804127708216557568 |
|---|---|
| adam_text | Contents
Introduction 1
Remarks on Notation and Terminology 3
Chapter 1 Basics 7
1.1 The Definitions 7
1.2 Fields and Vector Spaces 16
1.3 Matrices 27
1.4 Modules 31
1.5 The Language of Categories 43
Chapter 2 Linear Algebras and Artinian Rings 53
2.1 Linear Algebras 53
2.2 Chain Conditions 59
2.3 Artinian Rings: the Semisimple Case 66
2.4 Artinian Rings: the Radical 75
2.5 The Krull Schmidt Theorem 80
2.6 Group Representations. Definitions and General Properties .... 84
2.7 Group Characters 94
Chapter 3 Noetherian Rings 103
3.1 Polynomial Rings 103
3.2 The Euclidean Algorithm 109
3.3 Factorization 115
3.4 Principal Ideal Domains 120
ix
x Introduction to Ring Theory
3.5 Modules over Principal Ideal Domains 125
3.6 Algebraic Integers 130
Chapter 4 Ring Constructions 135
4.1 The Direct Product of Rings 135
4.2 The Axiom of Choice and Zorn s Lemma 140
4.3 Tensor Products of Modules and Algebras 143
4.4 Modules over General Rings 150
4.5 Projective Modules 156
4.6 Injective Modules 163
4.7 Invariant Basis Number and Projective Free Rings 169
Chapter 5 General Rings 175
5.1 Rings of Fractions 175
5.2 Skew Polynomial Rings 181
5.3 Free Algebras and Tensor Rings 188
5.4 Free Ideal Rings 197
Outline Solutions 203
Notations and Symbols 219
Bibliography 223
Index 225
|
| any_adam_object | 1 |
| author | Cohn, Paul M. 1924-2006 |
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| ctrlnum | (OCoLC)42009392 (DE-599)BVBBV013006761 |
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| 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 |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:37:38Z |
| institution | BVB |
| isbn | 1852332069 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008864603 |
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| physical | X, 229 S. graph. Darst. 24 cm |
| publishDate | 2000 |
| publishDateSearch | 2000 |
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| publisher | Springer |
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| series2 | Springer undergraduate mathematics series |
| spelling | Cohn, Paul M. 1924-2006 Verfasser (DE-588)121230538 aut Introduction to ring theory P. M. Cohn London ; Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong Springer 2000 X, 229 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Springer undergraduate mathematics series Anneaux (Algèbre) Ringen (wiskunde) gtt Rings (Algebra) Ringtheorie (DE-588)4126571-3 gnd rswk-swf Ringtheorie (DE-588)4126571-3 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008864603&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cohn, Paul M. 1924-2006 Introduction to ring theory Anneaux (Algèbre) Ringen (wiskunde) gtt Rings (Algebra) Ringtheorie (DE-588)4126571-3 gnd |
| subject_GND | (DE-588)4126571-3 |
| title | Introduction to ring theory |
| title_auth | Introduction to ring theory |
| title_exact_search | Introduction to ring theory |
| title_full | Introduction to ring theory P. M. Cohn |
| title_fullStr | Introduction to ring theory P. M. Cohn |
| title_full_unstemmed | Introduction to ring theory P. M. Cohn |
| title_short | Introduction to ring theory |
| title_sort | introduction to ring theory |
| topic | Anneaux (Algèbre) Ringen (wiskunde) gtt Rings (Algebra) Ringtheorie (DE-588)4126571-3 gnd |
| topic_facet | Anneaux (Algèbre) Ringen (wiskunde) Rings (Algebra) Ringtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008864603&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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