UID:
almahu_9947359995402882
Format:
Online-Ressource
Edition:
2nd revised and extended edition 2011
Edition:
Online-Ausg. 2011
ISBN:
9783110215205
Series Statement:
de Gruyter Expositions in Mathematics 30
Content:
This is the second revised edition of an introduction to contemporary relative homological algebra. It supplies important material essential to understand topics in algebra, algebraic geometry and algebraic topology. Each section comes with exercises providing practice problems for students as well as additional important results for specialists. The book is also suitable for an introductory course in commutative and ordinary homological algebra
Note:
Includes bibliographical references and index
,
11.4 Gorenstein Essential Extensions11.5 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; 11.9 Kaplansky Classes; 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;.
,
3.2 Natural Identities, Flat Modules, and Injective Modules3.3 Injective Modules over Commutative Noetherian Rings; 3.4 Matlis Duality; 4 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 Envelopes6.6 Existence of Envelopes for Injective Structures; 6.7 Pure Injective Envelopes; 7 Covers, Envelopes, and Cotorsion Theories; 7.1 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 µ-dimensions.
,
9 Iwanaga-Gorenstein and Cohen-Macaulay Rings and Their Modules9.1 Iwanaga-Gorenstein Rings; 9.2 The Minimal Injective Resolution of R; 9.3 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.
,
Preface; Preface to the Second Edition; 1 Basic Concepts; 1.1 Zorn's Lemma, Ordinal and Cardinal Numbers; 1.2 Modules; 1.3 Tensor Products of Modules and Nakayama Lemma; 1.4 Categories and Functors; 1.5 Complexes of Modules and Homology; 1.6 Direct and Inverse Limits; 1.7 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.
Additional Edition:
ISBN 9783110215212
Language:
English
DOI:
10.1515/9783110215212
URL:
http://www.degruyter.com/doi/book/10.1515/9783110215212
URL:
Volltext
(lizenzpflichtig)
