Introduction to Homological Algebra, 85 (Google eBook)

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Academic Press, Sep 7, 1979 - Mathematics - 400 pages
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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. Homological algebra is an accessible subject to those who wish to learn it, and this book is the authorís attempt to make it lovable.
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 ?; 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.
  

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Contents

Chapter 1 Introduction
1
Chapter 2 Hom and
23
Chapter 3 Projectives Injectives and Flats
57
Chapter 4 Specific Rings
108
Chapter 5 Extensions of Groups
150
Chapter 6 Homology
166
Chapter 7 Ext
194
Chapter 8 Tor
220
Chapter 9 Son of Specific Rings
232
Chapter 10 The Return of Cohomology of Groups
265
Chapter 11 Spectral Sequences
299
References
367
Index
371
Pure and Applied Mathematics
377
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Algebra
Serge Lang
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