Introduction to Homological Algebra
Edition: 2nd 2009
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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 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.
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All the information you need in one place! Each Study Brief is a summary of one specific subject; facts, figures, and explanations to help you learn faster.
Copyright year: 2009
Publication date: 10/14/2008
Size: 6.25" wide x 9.00" long x 1.50" tall
|Preface to the Second Edition|
|How to Read This Book|
|Categories and Functors|
|Hom and Tensor|
|von Neumann Regular Rings|
|Hereditary and Dedekind Rings|
|Semihereditary and Prufer Rings|
|Setting the Stage|
|Adjoint Functor Theorem for Modules|
|Left Derived Functors|
|Covariant Right Derived Functors|
|Contravariant Right Derived Functors|
|Tor and Ext|
|Homology and Rings|
|Dimensions of Rings|
|Hilbert's Syzygy Theorem|
|Stably Free Modules|
|Commutative Noetherian Local Rings|
|Homology and Groups|
|General Extensions and Cohomology|
|Change of Groups|
|Restriction and Inflation|
|Outer Automorphisms of p-Groups|
|Division Rings and Brauer Groups|
|Filtrations and Exact Couples|
|Homology of the Total Complex|
|Grothendieck Spectral Sequences|