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Introduction to Homological Algebra, 85
- 1st Edition - June 28, 1979
- Author: Joseph J. Rotman
- Language: English
- Hardback ISBN:9 7 8 - 0 - 1 2 - 5 9 9 2 5 0 - 3
- eBook ISBN:9 7 8 - 0 - 0 8 - 0 8 7 4 0 1 - 2
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… Read more
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Request a sales quoteAn 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 author’s 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.
PrefaceContents1. Introduction Line Integrals and Independence of Path Categories and Functors Tensor Products Singular Homology2. Hom and Ⓧ Modules Sums and Products Exactness Adjoints Direct Limits Inverse Limits3. Projectives, Injectives, and Flats Free Modules Projective Modules Injective Modules Watts’ Theorems Flat Modules Purity Localization4. Specific Rings Noetherian Rings Semisimple Rings Von Neumann Regular Rings Hereditary and Dedekind Rings Semihereditary and Prüfer Rings Quasi-Frobenius Rings Local Rings and Artinian Rings Polynomial Rings5. Extensions of Groups6. Homology Homology Functors Derived Functors7. Ext Elementary Properties Ext and Extensions Axioms8. Tor Elementary Properties Tor and Torsion Universal Coefficient Theorems9. Son of Specific Rings Dimensions Hilbert's Syzygy Theorem Serre's Theorem Mixed Identities Commutative Noetherian Local Rings10. The Return of Cohomology of Groups Homology Groups Cohomology Groups Computations and Applications11. Spectral Sequences Exact Couples and Five-Term Sequences Derived Couples and Spectral Sequences Filtrations and Convergence Bicomplexes Künneth Theorems Grothendieck Spectral Sequences More Groups More ModulesReferencesIndex
- No. of pages: 400
- Language: English
- Edition: 1
- Published: June 28, 1979
- Imprint: Academic Press
- Hardback ISBN: 9780125992503
- eBook ISBN: 9780080874012
JR
Joseph J. Rotman
Affiliations and expertise
University of Illinois, UrbanaRead Introduction to Homological Algebra, 85 on ScienceDirect