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Relative Homological Algebra.
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin :
De Gruyter,
2000.
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| Colección: | Gruyter Expositions in Mathematics.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Preface; 1 Basic Concepts; 1.1 Zorn's lemma, ordinal and cardinal numbers; 1.2 Modules; 1.3 Categories and functors; 1.4 Complexes of modules and homology; 1.5 Direct and inverse limits; 1.6 I-adic topology and completions; 2 Flat Modules, Chain Conditions and Prime Ideals; 2.1 Flat modules; 2.2 Localization; 2.3 Chain conditions; 2.4 Prime ideals and primary decomposition; 2.5 Artin-Rees lemma and Zariski rings; 3 Injective and Flat Modules; 3.1 Injective modules; 3.2 Natural identities, flat modules, and injective modules; 3.3 Injective modules over commutative noetherian rings.
- 3.4 Matlis duality4 Torsion Free Covering Modules; 4.1 Existence of torsion free precovers; 4.2 Existence of torsion free covers; 4.3 Examples; 4.4 Direct sums and products; 5 Covers; 5.1 F-precovers and covers; 5.2 Existence of precovers and covers; 5.3 Projective and flat covers; 5.4 Injective covers; 5.5 Direct sums and T-nilpotency; 6 Envelopes; 6.1 F-preenvelopes and envelopes; 6.2 Existence of preenvelopes; 6.3 Existence of envelopes; 6.4 Direct sums of envelopes; 6.5 Flat envelopes; 6.6 Existence of envelopes for injective structures; 6.7 Pure injective envelopes.
- 7 Covers, Envelopes, and Cotorsion Theories7.1 Definitions and basic results; 7.2 Fibrations, cofibrations and Wakamatsu lemmas; 7.3 Set theoretic homological algebra; 7.4 Cotorsion theories with enough injectives and projectives; 8 Relative Homological Algebra and Balance; 8.1 Left and right F-resolutions; 8.2 Derived functors and balance; 8.3 Applications to modules; 8.4 F-dimensions; 8.5 Minimal pure injective resolutions of flat modules; 8.6? and æ-dimensions; 9 Iwanaga-Gorenstein and Cohen-Macaulay Rings and Their Modules; 9.1 Iwanaga-Gorenstein rings.
- 9.2 The minimal injective resolution of R9.3 More on flat and injective modules; 9.4 Torsion products of injective modules; 9.5 Local cohomology and the dualizing module; 10 Gorenstein Modules; 10.1 Gorenstein injective modules; 10.2 Gorenstein projective modules; 10.3 Gorenstein flat modules; 10.4 Foxby classes; 11 Gorenstein Covers and Envelopes; 11.1 Gorenstein injective precovers and covers; 11.2 Gorenstein injective preenvelopes; 11.3 Gorenstein injective envelopes; 11.4 Gorenstein essential extensions; 11.5 Gorenstein projective precovers and covers.
- 11.6 Auslander's last theorem (Gorenstein projective covers)11.7 Gorenstein flat covers; 11.8 Gorenstein flat and projective preenvelopes; 12 Balance over Gorenstein and Cohen-Macaulay Rings; 12.1 Balance of Hom( -,
- ); 12.2 Balance of -? -; 12.3 Dimensions over n-Gorenstein rings; 12.4 Dimensions over Cohen-Macaulay rings; 12.5 O-Gorenstein modules; Bibliographical Notes; Bibliography; Index.