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.
Jenda / Enochs
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Zielgruppe
Lecturers, Graduate Students of Mathematics; Academic Libraries
Weitere Infos & Material
Frontmatter
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
Edgar E. Enochs, University of Kentucky, Lexington, USA; Overtoun M. G. Jenda, Auburn University, Alabama, USA.
