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Basic Homological Algebra

  • Textbook
  • © 2000

Overview

Authors:
  1. M. Scott Osborne

    1. Department of Mathematics, University of Washington, Seattle, USA

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Part of the book series: Graduate Texts in Mathematics (GTM, volume 196)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-x
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  2. Categories

    • M. Scott Osborne
    Pages 1-10

  3. Modules

    • M. Scott Osborne
    Pages 11-38

  4. Ext and Tor

    • M. Scott Osborne
    Pages 39-72

  5. Dimension Theory

    • M. Scott Osborne
    Pages 73-97

  6. Change of Rings

    • M. Scott Osborne
    Pages 99-121

  7. Derived Functors

    • M. Scott Osborne
    Pages 123-163

  8. Abstract Homological Algebra

    • M. Scott Osborne
    Pages 165-255

  9. Colimits and Tor

    • M. Scott Osborne
    Pages 257-284

  10. Odds and Ends

    • M. Scott Osborne
    Pages 285-335

  11. Back Matter

    Pages 337-398
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Keywords

About this book

Five years ago, I taught a one-quarter course in homological algebra. I discovered that there was no book which was really suitable as a text for such a short course, so I decided to write one. The point was to cover both Ext and Tor early, and still have enough material for a larger course (one semester or two quarters) going off in any of several possible directions. This book is 'also intended to be readable enough for independent study. The core of the subject is covered in Chapters 1 through 3 and the first two sections ofChapter 4. At that point there are several options. Chapters 4 and 5 cover the more traditional aspects of dimension and ring changes. Chapters 6 and 7 cover derived functors in general. Chapter 8 focuses on a special property of Tor. These three groupings are independent, as are various sections from Chapter 9, which is intended as a source of special topics. (The prerequisites for each section of Chapter 9 are stated at the beginning.) Some things have been included simply because they are hard to find else­ where, and they naturally fit into the discussion. Lazard's theorem (Section 8.4)-is an example; Sections4,5, and 7ofChapter 9 containother examples, as do the appendices at the end.

Reviews

“Each chapter contains a reasonable selection of exercises. … its intended audience is second or third year graduate students in algebra, algebraic topology, or other fields that use homological algebra. … the author’s style is both readable and entertaining … . All in all, this book is a very welcome addition to the literature.” (T.W.Hungerford, zbMATH 0948.18001, 2022)




"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

Authors and Affiliations

  • Department of Mathematics, University of Washington, Seattle, USA

    M. Scott Osborne

Bibliographic Information

  • Book Title: Basic Homological Algebra

  • Authors: M. Scott Osborne

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-1278-2

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 2000

  • Hardcover ISBN: 978-0-387-98934-1Published: 19 May 2000

  • Softcover ISBN: 978-1-4612-7075-1Published: 18 September 2012

  • eBook ISBN: 978-1-4612-1278-2Published: 06 December 2012

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: X, 398

  • Topics: K-Theory

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