Covers and envelopes in the category of complexes of modules:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Chapman & Hall/CRC
1999
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| Series: | Chapman & Hall CRC research notes in mathematics series
407 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 137 S. |
| ISBN: | 158488004X |
Staff View
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Record in the Search Index
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| adam_text | Contents
1. Covers and Envelopes in Categories 1
1.1 Zorn s Lemma for Categories 1
1.2 Torsion Theory Relative to Ext 6
1.2.1 The Definition of Torsion Theory Relative to Ext 6
1.2.2 Examples 11
1.2.3 Hereditary and Perfect Torsion Theories 12
1.2.4 Torsion Theories and Balance 19
1.3 Preserving and Reflecting Covers by Functors 21
2. Orthogonality in the Category of Complexes 32
2.1 Introduction 32
2.2 Spaltenstein s Quasi Isomorphisms 34
2.3 Exact, DG Injective and DG Projective
Covers and Envelopes 38
2.4 Minimal Injective Resolutions 47
3. Gorenstein Injective and Projective Complexes 52
3.1 Preliminaries 52
3.2 Gorenstein Injective Complexes 55
3.2.1 Existence of Envelopes 60
3.2.2 Existence of DG Injective and Gorenstein Injective
Covers 64
3.3 Gorenstein Projective Complexes 69
3.3.1 Auslander s Last Theorem 74
4. Flat and DG Flat Complexes 81
4.1 First Definitions and Results 81
4.2 Some Canonical Isomorphisms 87
4.3 Flat Covers of Complexes 96
4.3.1 Existence of Flat Covers of Complexes Over 7Z 97
4.3.2 Cotorsion Complexes 98
4.4 Existence of Flat Covers of Complexes Over a Commutative Noetherian
Ring with Finite Krull Dimension 100
4.4.1 DG Flat Covers 104
5. Pure Sequences of Complexes 108
5.1 Preliminaires 108
5.2 Flat Preenvelope of Complexes 110
5.3 Pure Injective and Cotorsion Envelopes 113
5.4 Gorenstein Flat Complexes 117
5.4.1 Existence of Gorenstein Flat Covers 122
5.5 A Theorem on Perfect Rings 124
5.6 DG Pure Sequences 127
Bibliography 133
Index 135
|
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| id | DE-604.BV013549958 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:47:48Z |
| institution | BVB |
| isbn | 158488004X |
| language | English |
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| physical | 137 S. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series | Chapman & Hall CRC research notes in mathematics series |
| series2 | Chapman & Hall CRC research notes in mathematics series |
| spelling | García Rozas, Juan R. Verfasser aut Covers and envelopes in the category of complexes of modules J. R. García Rozas Boca Raton [u.a.] Chapman & Hall/CRC 1999 137 S. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall CRC research notes in mathematics series 407 Categorieën (wiskunde) gtt Catégorie Catégorie complexe Catégories (mathématiques) ram Complexe plat Complexe projectif Modulen (wiskunde) gtt Revêtement complexe module Suite pure complexe Categories (Mathematics) Complexes Modules (Algebra) Chapman & Hall CRC research notes in mathematics series 407 (DE-604)BV012456897 407 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009252285&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | García Rozas, Juan R. Covers and envelopes in the category of complexes of modules Chapman & Hall CRC research notes in mathematics series Categorieën (wiskunde) gtt Catégorie Catégorie complexe Catégories (mathématiques) ram Complexe plat Complexe projectif Modulen (wiskunde) gtt Revêtement complexe module Suite pure complexe Categories (Mathematics) Complexes Modules (Algebra) |
| title | Covers and envelopes in the category of complexes of modules |
| title_auth | Covers and envelopes in the category of complexes of modules |
| title_exact_search | Covers and envelopes in the category of complexes of modules |
| title_full | Covers and envelopes in the category of complexes of modules J. R. García Rozas |
| title_fullStr | Covers and envelopes in the category of complexes of modules J. R. García Rozas |
| title_full_unstemmed | Covers and envelopes in the category of complexes of modules J. R. García Rozas |
| title_short | Covers and envelopes in the category of complexes of modules |
| title_sort | covers and envelopes in the category of complexes of modules |
| topic | Categorieën (wiskunde) gtt Catégorie Catégorie complexe Catégories (mathématiques) ram Complexe plat Complexe projectif Modulen (wiskunde) gtt Revêtement complexe module Suite pure complexe Categories (Mathematics) Complexes Modules (Algebra) |
| topic_facet | Categorieën (wiskunde) Catégorie Catégorie complexe Catégories (mathématiques) Complexe plat Complexe projectif Modulen (wiskunde) Revêtement complexe module Suite pure complexe Categories (Mathematics) Complexes Modules (Algebra) |
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