Part of the Universitext book series UTX. With a wealth of examples as well as abundant applications to Algebra, this is a must-read work: a clearly written, easy-to-follow guide to Homological Algebra. The author provides a treatment of Homological Algebra which approaches the subject in terms of its origins in algebraic topology. In this brand new edition the text has been fully updated and revised throughout and new material on sheaves and abelian categories has been added. Learning Homological Algebra is a two-stage affair. Firstly, one must learn the language of Ext and Tor, and what this describes.
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Introduction to Homological Algebra, Joseph J. An Introduction to Homological Algebra discusses the origins of algebraic topology.
It also presents the study of homological algebra as a two-stage affair. First, one must learn the language of Ext and Tor and what it describes. Second, one must be able to compute these things, and often, this involves yet another language: spectral sequences.
This book comprises 11 chapters, with an introductory chapter that focuses on line integrals and independence of path, categories and functors, tensor products, and singular homology. Succeeding chapters discuss Hom and X; projectives, injectives, and flats; specific rings; extensions of groups; homology; Ext; Tor; son of specific rings; the return of cohomology of groups; and spectral sequences, such as bicomplexes, Kunneth Theorems, and Grothendieck Spectral Sequences.
This book will be of interest to practitioners in the field of pure and applied mathematics. Chapter 2 Hom and. Chapter 3 Projectives Injectives and Flats. Chapter 4 Specific Rings. Chapter 5 Extensions of Groups. Chapter 6 Homology. Chapter 9 Son of Specific Rings. Chapter 10 The Return of Cohomology of Groups. Chapter 11 Spectral Sequences. Pure and Applied Mathematics. Rings and Categories of Modules Frank W. Anderson , Kent R.
Introduction to Homological Algebra, 85 Joseph J. Chapter 1 Introduction. Chapter 7 Ext. Chapter 8 Tor.
Introduction to Homological Algebra, 85
Introduction to Homological Algebra, Joseph J. An Introduction to Homological Algebra discusses the origins of algebraic topology. It also presents the study of homological algebra as a two-stage affair.
An Introduction to Homological Algebra
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