Basic Homological Algebra / Edition 1

Basic Homological Algebra / Edition 1

by M. Scott Osborne
     
 

From the reviews: "The book is well written. We find here many examples. Each chapter is followed by exercises, and at the end of the book there are outline solutions to some of them. [...] I especially appreciated the lively style of the book; […] one is quickly able to find necessary details." EMS NewsletterSee more details below

Overview

From the reviews: "The book is well written. We find here many examples. Each chapter is followed by exercises, and at the end of the book there are outline solutions to some of them. [...] I especially appreciated the lively style of the book; […] one is quickly able to find necessary details." EMS Newsletter

Product Details

ISBN-13:
9780387989341
Publisher:
Springer New York
Publication date:
01/04/2008
Series:
Graduate Texts in Mathematics Series, #196
Edition description:
2000
Pages:
398
Product dimensions:
9.21(w) x 6.14(h) x 0.94(d)

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Meet the Author

Table of Contents

1 Categories.- 2 Modules.- 2.1 Generalities.- 2.2 Tensor Products.- 2.3 Exactness of Functors.- 2.4 Projectives, Injectives, and Flats.- 3 Ext and Tor.- 3.1 Complexes and Projective Resolutions.- 3.2 Long Exact Sequences.- 3.3 Flat Resolutions and Injective Resolutions.- 3.4 Consequences.- 4 Dimension Theory.- 4.1 Dimension Shifting.- 4.2 When Flats are Projective.- 4.3 Dimension Zero.- 4.4 An Example.- 5 Change of Rings.- 5.1 Computational Considerations.- 5.2 Matrix Rings.- 5.3 Polynomials.- 5.4 Quotients and Localization.- 6 Derived Functors.- 6.1 Additive Functors.- 6.2 Derived Functors.- 6.3 Long Exact Sequences—I. Existence.- 6.4 Long Exact Sequences—II. Naturality.- 6.5 Long Exact Sequences—III. Weirdness.- 6.6 Universality of Ext.- 7 Abstract Homologieal Algebra.- 7.1 Living Without Elements.- 7.2 Additive Categories.- 7.3 Kernels and Cokernels.- 7.4 Cheating with Projectives.- 7.5 (Interlude) Arrow Categories.- 7.6 Homology in Abelian Categories.- 7.7 Long Exact Sequences.- 7.8 An Alternative for Unbalanced Categories.- 8 Colimits and Tor.- 8.1 Limits and Colimits.- 8.2 Adjoint Functors.- 8.3 Directed Colimits,—, and Tor.- 8.4 Lazard’s Theorem.- 8.5 Weak Dimension Revisited.- 9 Odds and Ends.- 9.1 Injective Envelopes.- 9.2 Universal Coefficients.- 9.3 The Künneth Theorems.- 9.4 Do Connecting Homomorphisms Commute?.- 9.5 The Ext Product.- 9.6 The Jacobson Radical, Nakayama’s Lemma, and Quasilocal Rings.- 9.7 Local Rings and Localization Revisited (Expository).- A GCDs, LCMs, PIDs, and UFDs.- B The Ring of Entire Functions.- C The Mitchell—Freyd Theorem and Cheating in Abelian Categories.- D Noether Correspondences in Abelian Categories.- Solution Outlines.- References.- Symbol Index.

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