# Basic Homological Algebra

Textbook

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

1. Front Matter
Pages i-x
2. M. Scott Osborne
Pages 1-10
3. M. Scott Osborne
Pages 11-38
4. M. Scott Osborne
Pages 39-72
5. M. Scott Osborne
Pages 73-97
6. M. Scott Osborne
Pages 99-121
7. M. Scott Osborne
Pages 123-163
8. M. Scott Osborne
Pages 165-255
9. M. Scott Osborne
Pages 257-284
10. M. Scott Osborne
Pages 285-335
11. Back Matter
Pages 337-398

### Introduction

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.

### Keywords

Adjoint functor Homological algebra algebra colimit homomorphism

#### Authors and affiliations

1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA

### 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
• Copyright Information Springer-Verlag New York, Inc. 2000
• Publisher Name Springer, New York, NY
• eBook Packages
• Hardcover ISBN 978-0-387-98934-1
• Softcover ISBN 978-1-4612-7075-1
• eBook ISBN 978-1-4612-1278-2
• Series ISSN 0072-5285
• Edition Number 1
• Number of Pages X, 398
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site

## 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."