Graduate Texts in Mathematics

By: M. Scott Osborne

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Hardcover | 1 June 2000

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416 Pages

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23.39 x 15.6 x 2.39

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This book is intended for one-quarter or one semester-courses in homological algebra. The aim is to cover Ext and Tor early and without distraction. It includes several further topics, which can be pursued independently of each other. Many of these, such as Lazard's theorem, long exact sequences in Abelian categories with no cheating, or the relation between Krull dimension and global dimension, are hard to find elsewhere. The intended audience is second or third year graduate students in algebra, algebraic topology, or any other field that uses homological algebra.

Industry 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; compared with some other books on homological algebra, one has here the good feeling that one understands why a notion is defined in this way, that one can easily remember at least the structure of the theory, and that one is quickly able to find necessary details. The prerequisite for this book is a graduate course on algebra, but one get quite far with a modest knowledge of algebra. The book can be strongly recommended as a textbook for a course on homological algebra."
EMS Newsletter, June 2001

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Preface
Categories	p. 1
Modules	p. 11
Generalities	p. 11
Tensor Products	p. 14
Exactness of Functors	p. 22
Projectives, Injectives, and Flats	p. 28
Ext and Tor	p. 39
Complexes and Projective Resolutions	p. 39
Long Exact Sequences	p. 47
Flat Resolutions and Injective Resolutions	p. 55
Consequences	p. 66
Dimension Theory	p. 73
Dimension Shifting	p. 73
When Flats are Projective	p. 79
Dimension Zero	p. 82
Change of Rings	p. 99
Computational Considerations	p. 99
Matrix Rings	p. 104
Polynomials	p. 106
Quotients and Localization	p. 110
Derived Functors	p. 123
Additive Functors	p. 123
Derived Functors	p. 126
Long Exact Sequences - I. Existence	p. 130
Long Exact Sequences - II. Naturality	p. 140
Long Exact Sequences - III. Weirdness	p. 147
Universality of Ext	p. 151
Abstract Homological Algebra	p. 165
Living Without Elements	p. 165
Additive Categories	p. 169
Kernels and Cokernels	p. 173
Cheating with Projectives	p. 186
(Interlude) Arrow Categories	p. 202
Homology in Abelian Categories	p. 213
Long Exact Sequences	p. 225
An Alternative for Unbalanced Categories	p. 239
Colimits and Tor	p. 257
Limits and Colimits	p. 257
Adjoint Functors	p. 264
Directed Colimits, [actual symbol not reproducible], and Tor	p. 270
Lazard's Theorem	p. 274
Weak Dimension Revisited	p. 280
Odds and Ends	p. 285
Injective Envelopes	p. 285
Universal Coefficients	p. 290
The Kunneth Theorems	p. 296
Do Connecting Homomorphisms Commute?	p. 309
The Ext Product	p. 318
The Jacobson Radical, Nakayama's Lemma and Quasilocal Rings	p. 324
Local Rings and Localization Revisited (Expository)	p. 331
GCDs, LCMs, PIDs, and UFDs	p. 337
The Ring of Entire Functions	p. 345
The Mitchell-Freyd Theorem and Cheating in Abelian Categories	p. 359
Noether Correspondences in Abelian Categories	p. 363
Solution Outlines	p. 373
References	p. 383
Symbol Index	p. 389
Index	p. 391
Table of Contents provided by Blackwell. All Rights Reserved.

Graduate Texts in Mathematics

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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