Relative homological algebra. Volume 1 / Edgar E. Enochs, Overtoun M.G. Jenda.

Format:

Book

Author/Creator:

Enochs, Edgar E.

Contributor:

Jenda, Overtoun M. G.

Series:

De Gruyter expositions in mathematics ; 30.

De Gruyter expositions in mathematics ; 30

Language:

English

Subjects (All):

Algebra, Homological.

Physical Description:

1 online resource (376 p.)

Edition:

2nd rev. and extended ed.

Place of Publication:

Berlin ; Boston : De Gruyter, c2011.

Language Note:

English

Summary:

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. In this new edition the authors have added well-known additional material in the first three chapters, and added new material that was not available at the time the original edition was published. In particular, the major changes are the following: Chapter 1: Section 1.2 has been rewritten to clarify basic notions for the beginner, and this has necessitated a new Section 1.3. Chapter 3: The classic work of D. G. Northcott on injective envelopes and inverse polynomials is finally included. This provides additional examples for the reader. Chapter 11: Section 11.9 on Kaplansky classes makes volume one more up to date. The material in this section was not available at the time the first edition was published. The authors also have clarified some text throughout the book and updated the bibliography by adding new references. The book is also suitable for an introductory course in commutative and ordinary homological algebra.

Contents:

Front matter

Preface

Preface to the Second Edition

Contents

Chapter 1. Basic Concepts

Chapter 2. Flat Modules, Chain Conditions and Prime Ideals

Chapter 3. Injective and Flat Modules

Chapter 4. Torsion Free Covering Modules

Chapter 5. Covers

Chapter 6. Envelopes

Chapter 7. Covers, Envelopes, and Cotorsion Theories

Chapter 8. Relative Homological Algebra and Balance

Chapter 9. Iwanaga-Gorenstein and Cohen-Macaulay Rings and Their Modules

Chapter 10. Gorenstein Modules

Chapter 11. Gorenstein Covers and Envelopes

Chapter 12. Balance over Gorenstein and Cohen-Macaulay Rings

Bibliographical Notes

Bibliography

Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786613429032

9781283429030

1283429039

9783110215212

3110215217

OCLC:

769190340