Introduction to Homological Algebra

ISBN-10: 0387245278
ISBN-13: 9780387245270
Edition: 2nd 2009
Authors: Joseph J. Rotman
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Description: Learning homological algebra is 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  More...

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Book details

List price: $49.95
Edition: 2nd
Copyright year: 2009
Publisher: Springer
Publication date: 10/14/2008
Binding: Paperback
Pages: 710
Size: 6.25" wide x 9.00" long x 1.50" tall
Weight: 2.442

Learning homological algebra is 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 gives a treatment of homological algebra which motivates the subject in terms of its origins in algebraic topology. In this new edition the book has been updated and revised throughout and new material on sheaves and cup products has been added. The author also included material about homotopical algebra, alias K-theory, contrasting it with homological algebra.

Preface to the Second Edition
How to Read This Book
Introduction
Simplicial Homology
Categories and Functors
Singular Homology
Hom and Tensor
Modules
Tensor Products
Adjoint Isomorphisms
Special Modules
Projective Modules
Injective Modules
Flat Modules
Purity
Specific Rings
Semisimple Rings
von Neumann Regular Rings
Hereditary and Dedekind Rings
Semihereditary and Prufer Rings
Quasi-Frobenius Rings
Semiperfect Rings
Localization
Polynomial Rings
Setting the Stage
Categorical Constructions
Limits
Adjoint Functor Theorem for Modules
Sheaves
Manifolds
Sheaf Constructions
Abelian Categories
Complexes
Homology
Homology Functors
Derived Functors
Left Derived Functors
Axioms
Covariant Right Derived Functors
Contravariant Right Derived Functors
Sheaf Cohomology
Cech Cohomology
Riemann-Roch Theorem
Tor and Ext
Tor
Domains
Localization
Ext
Baer Sum
Cotorsion Groups
Universal Coefficients
Homology and Rings
Dimensions of Rings
Hilbert's Syzygy Theorem
Stably Free Modules
Commutative Noetherian Local Rings
Homology and Groups
Group Extensions
Semidirect Products
General Extensions and Cohomology
Stabilizing Automorphisms
Group Cohomology
Bar Resolutions
Group Homology
Schur Multiplier
Change of Groups
Restriction and Inflation
Transfer
Tate Groups
Outer Automorphisms of p-Groups
Cohomological Dimension
Division Rings and Brauer Groups
Spectral Sequences
Bicomplexes
Filtrations and Exact Couples
Convergence
Homology of the Total Complex
Cartan-Eilenberg Resolutions
Grothendieck Spectral Sequences
Groups
Rings
Sheaves
Kunneth Theorems
References
Special Notation
Index

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