Gorenstein Homological Algebra 1st Edition by Alina Iacob ISBN 1138065498 9781138065499

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Product details:

ISBN 10:      1138065498
ISBN 13: 978-1138065499
Author:      Alina Iacob

Gorenstein Homological Algebra 1st Table of contents:

 

1. Modules – Projective, Injective, and Flat Modules
1.1 Modules
1.2 Tensor Product
1.3 Complexes of Modules
1.4 Categories and Functors
1.5 Localization
1.6 Noetherian Rings. Artinian Rings
1.7 Projective and Flat Modules
1.8 Injective Modules
1.9 Precovers and Covers. Preenvelopes and Envelopes
1.10 Cotorsion Pairs. Duality Pairs
1.11 Triangulated Categories
1.12 Derived Category

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2. Gorenstein Projective, Injective, and Flat Modules
2.1 Totally Reflexive Modules
2.2 Gorenstein Projective Modules – Definition and Properties
2.3 Gorenstein Injective Modules – Definition and Properties
2.4 Gorenstein Flat Modules – Definition and Properties

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3. Gorenstein Projective Resolutions
3.1 Gorenstein Projective Precovers. Left Gorenstein Projective Resolutions
3.2 Examples of Non-Coherent Rings that are Left GF-Closed
3.3 Gorenstein Projective (Pre)envelopes. Right Gorenstein Projective Resolutions

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4. Gorenstein Injective Resolutions
4.1 Gorenstein Injective Envelopes
4.2 Gorenstein Injective Covers
4.3 Rings with the Property that Character Modules of Gorenstein Injective Left R-Modules are Gorenstein Flat

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5. Gorenstein Flat Precovers and Preenvelopes
5.1 Gorenstein Flat Precovers
5.2 Gorenstein Flat Preenvelopes

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II. Connections with Tate (Co)homology
6.1 Balance in Tate Cohomology
6.2 Right Gorenstein Projective Resolutions and Tate Cohomology
6.3 Tate-Betti Numbers and Tate-Bass Numbers
6.4 Matlis Duality
6.5 A Generalization of Tate (Co)homology
6.6 Balance in Generalized Tate Cohomology
6.7 Tate Homology
6.8 Balance in Tate Homology. Computing Tate Homology Functors by Combined Use of Flat and Gorenstein Flat Resolutions of M

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7. Totally Acyclic Complexes
7.1 A-Persistent Modules
7.2 Totally Acyclic Complexes of Injective, Projective, and Flat Modules
7.3 Total Acyclicity over Rings that Satisfy the Auslander Condition

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8. Generalizations of the Gorenstein Modules
8.1 Ding Projective and Ding Injective Modules
8.2 FPn-Injective and FPn-Flat Modules. Absolutely Clean Modules; Level Modules
8.3 Gorenstein AC-Projective, Injective, and Flat Modules

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9. Gorenstein Projective, Injective, Flat Complexes, dg-Projective, dg-Injective, dg-Flat Complexes
9.1 Projective, Injective, and Flat Complexes
9.2 Dg-Injective, Dg-Projective, Dg-Flat Complexes. Dw-Injective, Dw-Projective, and Dw-Flat Complexes
9.3 Complexes of Injective Modules
9.4 Complexes of Flat Modules and of Projective Modules
9.5 Gorenstein Injective, Projective, and Flat Complexes
9.6 When is DwC Covering?
9.7 Gorenstein Injective, Projective, and Flat Precovers and Preenvelopes in Ch(R)
9.8 Gorenstein Cohomology for Complexes. Generalized Tate Cohomology for Complexes

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