Introduction to Homological Algebra, 85
Published on 7. September 1979
Book
Hardback
400 pages
978-0-12-599250-3 (ISBN)
Description
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 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.
More details
Language
English
Place of publication
San Diego
United States
Publishing group
Elsevier Science Publishing Co Inc
Target group
Professional and scholarly
Product notice
Laminated cover
Dimensions
Height: 235 mm
Width: 161 mm
Thickness: 34 mm
Weight
771 gr
ISBN-13
978-0-12-599250-3 (9780125992503)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Rotman | Joseph J. Rotman
Introduction to Homological Algebra, 85
E-Book
05/2014
Academic Press
€54.95
Available for download
Person
Content
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 Pruefer 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 Kuenneth Theorems Grothendieck Spectral Sequences More Groups More ModulesReferencesIndex