Modules and the structure of rings: a primer
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Dekker
1991
|
| Series: | Pure and applied mathematics
147 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 263 S. |
| ISBN: | 082478555X |
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MARC
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| 245 | 1 | 0 | |a Modules and the structure of rings |b a primer |c Jonathan S. Golan ; Tom Head |
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| 300 | |a XV, 263 S. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface v
Introduction xiii
Fundamental Concepts
CHAPTER 0. MODULES AND MAPS
1. Modules 3
2. Submodules and factor modules 7
3. Direct products and coproducts 10
4. Homomorphisms of modules 12
5. Bimodules 17
6. Projections and injections 20
7. Internal direct sums 26
8. Splitting maps and sumrnands 29
9. Natural maps 31
10. Subsets and the submodules they generate 34
11. Maximal nests of subsets 36
CHAPTER 1. THE RING AS A MODULE OVER ITSELF
1. Introduction 39
2. Modules associated with R 40
3. Using the identity of R (projectivity) 47
vii
viii Contents
Part One: Projectivity
CHAPTER 2. COPRODUCTS OF COPIES OF R
(FREE MODULES)
1. Introduction 55
2. Bases 56
3. Independent sets 62
4. Division rings 66
Notes for Chapter 2 71
CHAPTER 3. DIRECT SUMMANDS OF FREE MODULES
(PROJECTIVE MODULES)
1. Introduction 73
2. Semisimple rings 76
3. Matrix rings 81
4. Group rings 84
Notes for Chapter 3 88
CHAPTER 4. SUBMODULES OF FREE MODULES
1. Introduction 91
2. Hereditary rings 92
3. Hereditary rings (continued) 95
4. Principal ideal domains 97
Notes for Chapter 4 101
CHAPTER 5. FACTOR MODULES OF FREE MODULES
1. Introduction 103
2. Traces of projective modules 105
Part Two: Injectivity
CHAPTER 6. ENLARGING HOMOMORPHISMS
1. Introduction 111
2. The injectivity class of a module 113
3. Generators 117
Notes for Chapter 6 119
Contents ix
CHAPTER 7. EMBEDDING MODULES IN INJECTIVE
MODULES
1. Introduction 121
2. For noetherian rings 122
3. For arbitrary rings 125
4. Injective hulls 127
5. Divisible modules 133
Notes for Chapter 7 138
CHAPTER 8. INJECTIVE MODULES AS A CLASS
1. General closure properties 141
2. Cogenerators 142
3. Hereditary rings again 146
4. Noetherian rings 147
Notes for Chapter 8 151
CHAPTER 9. STRUCTURE OF INJECTIVE MODULES
1. Introduction 153
2. Uniform injective modules 154
3. Semiuniform injective modules 157
4. For principal ideal domains 161
5. For noetherian rings 163
6. Projective injectives and quasi Frobenius rings 168
Notes for Chapter 9 172
Part Three: Countability
CHAPTER 10. FINITELY GENERATED MODULES
1. Introduction 177
2. For principal ideal domains 179
Notes for Chapter 10 184
CHAPTER 11. COUNTABLY GENERATED MODULES
1. Introduction 185
2. Coproducts of finitely generated modules 186
3. Semihereditary rings 188
4. Rings of sets 192
Notes for Chapter 11 196
x Contents
CHAPTER 12. COPRODUCTS OF COUNTABLY
GENERATED MODULES
1. Introduction 199
2. Kaplansky s Theorem 200
CHAPTER 13. PROJECTIVE MODULES
1. Introduction 207
2. Local rings 210
Notes for Chapter 13 215
Part Four: Rings and modules of quotients
CHAPTER 14. TORSION AND TORSIONFREE
MODULES
1. Introduction 219
2. Equivalent injective modules 221
3. Torsionfree modules 225
4. Torsion modules 227
Notes for Chapter 14 233
CHAPTER 15. THE MODULE OF QUOTIENTS
1. Introduction 235
2. The module of quotients defined by equivalent
injective modules 236
3. The module of quotients defined by equivalent
projective modules 240
4. A representation of the module of quotients 243
Notes for Chapter 15 246
CHAPTER 16. RINGS OF QUOTIENTS
1. Introduction 247
2. Rings of quotients 247
Notes for Chapter 16 251
Contents xi
References 253
Index 261
|
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| physical | XV, 263 S. |
| publishDate | 1991 |
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| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Gôlān, Yônātān Verfasser aut Modules and the structure of rings a primer Jonathan S. Golan ; Tom Head New York [u.a.] Dekker 1991 XV, 263 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 147 Modul (DE-588)4129770-2 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Modul (DE-588)4129770-2 s DE-604 Head, Tom Verfasser aut Pure and applied mathematics 147 (DE-604)BV000001885 147 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002831305&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gôlān, Yônātān Head, Tom Modules and the structure of rings a primer Pure and applied mathematics Modul (DE-588)4129770-2 gnd |
| subject_GND | (DE-588)4129770-2 (DE-588)4151278-9 |
| title | Modules and the structure of rings a primer |
| title_auth | Modules and the structure of rings a primer |
| title_exact_search | Modules and the structure of rings a primer |
| title_full | Modules and the structure of rings a primer Jonathan S. Golan ; Tom Head |
| title_fullStr | Modules and the structure of rings a primer Jonathan S. Golan ; Tom Head |
| title_full_unstemmed | Modules and the structure of rings a primer Jonathan S. Golan ; Tom Head |
| title_short | Modules and the structure of rings |
| title_sort | modules and the structure of rings a primer |
| title_sub | a primer |
| topic | Modul (DE-588)4129770-2 gnd |
| topic_facet | Modul Einführung |
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