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Introduction to Homological Algebra, 85 by Joseph J. Rotman (1979, Hardcover)
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An Introduction to Homological Algebra discusses the origins of algebraic topology. 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.
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About this product
Product Identifiers
PublisherElsevier Science & Technology
ISBN-100125992505
ISBN-139780125992503
eBay Product ID (ePID)40788
Product Key Features
Number of Pages400 Pages
Publication NameIntroduction to Homological Algebra, 85
LanguageEnglish
SubjectAlgebra / Abstract, Topology
Publication Year1979
TypeTextbook
AuthorJoseph J. Rotman
Subject AreaMathematics
FormatHardcover
Dimensions
Item Weight25 Oz
Item Length9 in
Item Width6 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN78-020001
Volume NumberNo. 85
IllustratedYes
Table Of ContentPrefaceContents1. 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
SynopsisAn 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., 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."
LC Classification NumberQA3.P8 vol. 85
