The spectrum of a module category:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
AMS
2001
|
| Series: | American Mathematical Society: Memoirs of the American Mathematical Society
707 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | "Volume 149, number 707 (second of 4 numbers)." |
| Physical Description: | IX, 125 S. |
| ISBN: | 0821826182 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Chapter 0. Introduction 1
Chapter 1. The functor category 11
1.1. Preliminaries 11
1.2. Purity 12
Chapter 2. Definable subcategories 15
2.1. Definable subcategories 15
2.2. Saturation 18
2.3. The Ziegler topology 19
2.4. Definable quotient categories 20
2.5. Examples 22
Chapter 3. Left approximations 24
3.1. Left almost split maps 24
3.2. Left approximations 26
3.3. Minimal left approximations 28
Chapter 4. Duality 31
4.1. Purely equivalent and purely opposed modules 31
4.2. The dual of a definable subcategory 32
4.3. Pure reflexive modules 33
Chapter 5. Ideals in the category of finitely presented modules 37
5.1. Fp idempotent ideals 37
5.2. Ideals generated by idempotents 40
Chapter 6. Endofmite modules 43
6.1. The endocategory of a module 43
6.2. E pure injective modules 44
6.3. Product complete modules 45
6.4. Endofinite modules 46
6.5. Generic modules 49
6.6. Ideals of finite length 51
Chapter 7. Krull Gabriel dimension 54
7.1. The Krull Gabriel dimension of a ring 54
7.2. The Krull Gabriel dimension of a module 56
Chapter 8. The infinite radical 58
8.1. The preinjective dimension of a module 58
8.2. Transfinite powers of the Jacobson radical 60
vii
viii CONTENTS
Chapter 9. Functors between module categories 64
9.1. Coherent functors 64
Chapter 10. Tame algebras 68
10.1. Endofinitely tame algebras 68
10.2. Functors preserving tameness 69
10.3. Representation embeddings 71
10.4. One parameter families and generic modules 72
Chapter 11. Rings of definable scalars 73
11.1. Rings of definable scalars 73
11.2. Calculus of fractions 75
11.3. Biendomorphism rings 76
11.4. Basic properties 78
11.5. Epimorphisms of rings 79
Chapter 12. Reflective definable subcategories 82
12.1. Reflective definable subcategories 82
12.2. ^ continuous modules 84
12.3. Definable and universal localizations 86
Chapter 13. Sheaves 89
13.1. Sheaves on the Gabriel spectrum 89
13.2. The Zariski topology 93
13.3. Structure sheaves 94
13.4. Associated sheaves of modules 96
Chapter 14. Tame hereditary algebras 98
14.1. Preliminaries 98
14.2. A parametrizing curve 101
Chapter 15. Coherent rings 105
15.1. Preliminaries 105
15.2. Prime spectrum versus Gabriel spectrum 106
15.3. The global section functor 108
Appendix A. Locally coherent Grothendieck categories 111
A.I. Localization in abelian categories 111 •
A.2. Locally coherent Grothendieck categories 111
A.3. Localization in locally coherent Grothendieck categories 112
A.4. Locally noetherian categories 114
Appendix B. Dimensions 116
B.I. The dimension of an abelian category 116
B.2. The dimension of a modular lattice 117
Appendix C. Finitely presented functors and ideals 119
C.I. The category of finitely presented functors 119
C.2. Ideals in additive categories 120
Bibliography 122
|
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| id | DE-604.BV013626346 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:49:11Z |
| institution | BVB |
| isbn | 0821826182 |
| language | English |
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| physical | IX, 125 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | AMS |
| record_format | marc |
| series | American Mathematical Society: Memoirs of the American Mathematical Society |
| series2 | American Mathematical Society: Memoirs of the American Mathematical Society |
| spelling | Krause, Henning 1962- Verfasser (DE-588)1126055913 aut The spectrum of a module category Henning Krause Providence, RI AMS 2001 IX, 125 S. txt rdacontent n rdamedia nc rdacarrier American Mathematical Society: Memoirs of the American Mathematical Society 707 "Volume 149, number 707 (second of 4 numbers)." Categorieën (wiskunde) gtt Modulen (wiskunde) gtt Categories (Mathematics) Injective modules (Algebra) Kategorie Mathematik (DE-588)4129930-9 gnd rswk-swf Injektiver Modul (DE-588)4161753-8 gnd rswk-swf Injektiver Modul (DE-588)4161753-8 s Kategorie Mathematik (DE-588)4129930-9 s DE-604 American Mathematical Society: Memoirs of the American Mathematical Society 707 (DE-604)BV008000141 707 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009308818&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Krause, Henning 1962- The spectrum of a module category American Mathematical Society: Memoirs of the American Mathematical Society Categorieën (wiskunde) gtt Modulen (wiskunde) gtt Categories (Mathematics) Injective modules (Algebra) Kategorie Mathematik (DE-588)4129930-9 gnd Injektiver Modul (DE-588)4161753-8 gnd |
| subject_GND | (DE-588)4129930-9 (DE-588)4161753-8 |
| title | The spectrum of a module category |
| title_auth | The spectrum of a module category |
| title_exact_search | The spectrum of a module category |
| title_full | The spectrum of a module category Henning Krause |
| title_fullStr | The spectrum of a module category Henning Krause |
| title_full_unstemmed | The spectrum of a module category Henning Krause |
| title_short | The spectrum of a module category |
| title_sort | the spectrum of a module category |
| topic | Categorieën (wiskunde) gtt Modulen (wiskunde) gtt Categories (Mathematics) Injective modules (Algebra) Kategorie Mathematik (DE-588)4129930-9 gnd Injektiver Modul (DE-588)4161753-8 gnd |
| topic_facet | Categorieën (wiskunde) Modulen (wiskunde) Categories (Mathematics) Injective modules (Algebra) Kategorie Mathematik Injektiver Modul |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009308818&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT krausehenning thespectrumofamodulecategory |