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Graduate texts
in Mathematics
M. Scott Osborne
Basic
Homological
Algebra
Springer

Graduate Texts in Mathematics
196
Editorial Board
S. Axler
F.W. Gehring
K.A. Ribet
Springer
New York
Berlin
Heidelberg
Barcelona
Hong Kong
London
Milan
Paris
Singapore
Tokyo

Graduate Texts in Mathematics
1 TAKEUTI/ZARING. Introduction to
Axiomatic Set Theory. 2nd ed.
37
38
MONK. Mathematical Logic.
GRAUERT/FRITZSCHE. Several Complex
2 OxToBY. Measure and Category. 2nd ed.
Variables.
3 SCHAEFER. Topological Vector Spaces.
2nd ed.
39
40
ARVESON. An Invitation to C°-Algebras.
KEMENY/SNELL/KNAPP. Denumerable
4
HILTON/STAMMBACH. A Course in
Markov Chains. 2nd ed.
Homological Algebra. 2nd ed.
41
APOSTOL. Modular Functions and Dirichlet
5 MAC LANE. Categories for the Working
Mathematician. 2nd ed.
Series in Number Theory.
2nd ed.
6 HUGHES/PIPER. Projective Planes.
42
SERRE. Linear Representations of Finite
7 SERRE. A Course in Arithmetic.
Groups.
8
TAKEUTI/ZARING. Axiomatic Set Theory.
43
GILLMAN/JERISON. Rings of Continuous
9
HUMPHREYS. Introduction to Lie Algebras
and Representation Theory.
44
Functions.
KENDIG. Elementary Algebraic Geometry.
10
COHEN. A Course in Simple Homotopy
Theory.
45
46
LOEVE. Probability Theory I. 4th ed.
LOEVE. Probability Theory 11. 4th ed.
11
CONWAY. Functions of One Complex
Variable 1. 2nd ed.
47
MoISE. Geometric Topology in
Dimensions 2 and 3.
12 BEALS. Advanced Mathematical Analysis.
48
SACHS/WU. General Relativity for
13 ANDERSON/FULLER. Rings and Categories
Mathematicians.
of Modules. 2nd ed.
49
GRUENBERG/WEIR. Linear Geometry.
14
GOLUBITSKY/GUILLEMIN. Stable Mappings
and Their Singularities. 50
2nd ed.
EDWARDS. Fermat's Last Theorem.
15 BERBERIAN. Lectures in Functional
Analysis and Operator Theory.
51 KLINGENBERG. A Course in Differential
Geometry.
16 WINTER. The Structure of Fields. 52 HARTSHORNE. Algebraic Geometry.
17
ROSENBLATT. Random Processes. 2nd ed. 53 MANIN. A Course in Mathematical Logic.
18 HALMOS. Measure Theory. 54 GRAVER/WATKINS. Combinatorics with
19 HALMOS. A Hilbert Space Problem Book. Emphasis on the Theory of Graphs.
2nd ed. 55
BROWN/PEARCY. Introduction to Operator
20
HUSEMOLLER. Fibre Bundles. 3rd ed. Theory I: Elements of Functional
21 HUMPHREYS. Linear Algebraic Groups. Analysis.
22 BARNES/MACK, An Algebraic Introduction
to Mathematical Logic.
56
MASSEY. Algebraic Topology: An
Introduction.
23 GREUB. Linear Algebra. 4th ed. 57
CROWELL/Fox. Introduction to Knot
24 HOLMES. Geometric Functional Analysis Theory.
and Its Applications. 58 KoBLITZ. p-adic Numbers, p-adic Analysis,
25 HEWITT/STROMBERG. Real and Abstract
Analysis.
59
and Zeta-Functions. 2nd ed.
LANG. Cyclotomic Fields.
26
MANES. Algebraic Theories.
60
ARNOLD. Mathematical Methods in
27 KELLEY. General Topology.
Classical Mechanics. 2nd ed.
28 ZARISKI/SAMUEL. Commutative Algebra. 61
WHITEHEAD. Elements of Homotopy
Vol.l. 62
KARGAPOLOVIMERLZJAKOV. Fundamentals
29 ZARISKI/SAMUEL. Commutative Algebra.
Vol.I1.
63
of the Theory of Groups.
BOLLOBAS. Graph Theory.
30 JACOBSON. Lectures in Abstract Algebra I.
Basic Concepts.
64
65
EDWARDS. Fourier Series. Vol. 12nd ed.
WELLS. Differential Analysis on Complex
31
JACOBSON. Lectures in Abstract Algebra II.
Manifolds. 2nd ed.
Linear Algebra. 66
WATERHOUSE. Introduction to Affine
32
JACOBSON. Lectures in Abstract Algebra
III. Theory of Fields and Galois Theory.
67
Group Schemes.
SERRE. Local Fields.
33
HIRSCH. Differential Topology. 68
WEIDMANN. Linear Operators in Hilbert
34 SPITZER. Principles of Random Walk.
Spaces.
2nd ed.
69
LANG. Cyclotomic Fields II.
35 ALEXANDER/WERMER. Several Complex
Variables and Banach Algebras. 3rd ed.
70
71
MASSEY. Singular Homology Theory.
FARKAS/KRA. Riemann Surfaces. 2nd ed.
36
KELLEY/NAMIOKA et al. Linear Topological
Spaces.
(continued after index)

M. Scott Osborne
Basic Homological Algebra
Springer

M. Scott Osborne
Department of Mathematics
University of Washington
Seattle, WA 98195-4350 USA
sosbome@math.washington.edu
Editorial Board
S. Axler F.W. Gehring
K.A. Ribet
Mathematics Department
Mathematics Department
Mathematics Department
San Francisco State
East Hall
University of California
University University of Michigan
at Berkeley
San Francisco, CA 94132
Ann Arbor, MI 48109
Berkeley, CA 94720-3840
USA USA
USA
Mathematics Subject Classification (2000): 18-01, 18G15
Library of Congress Cataloging-in-Publication Data
Osborne, M. Scott.
Basic homological algebra / M. Scott Osborne.
p.
cm. - (Graduate texts in mathematics ; 196)
Includes bibliographical references and index.
ISBN 0-387-98934-X (hc. : alk. paper)
1. Algebra, Homological. I. Title. II. Series.
QAI69.083
2000
512'.55-dc2l
Printed on acid-free paper.
99-046582
© 2000 Springer-Verlag New York, Inc.
All rights reserved. This work may not be translated or copied in whole or in part without the
written permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York,
NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use
in connection with any form of information storage and retrieval, electronic adaptation, computer
software, or by similar or dissimilar methodology now known or hereafter developed is forbidden.
The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the
former are not especially identified, is not to be taken as a sign that such names, as understood by
the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone.
This reprint has been authorized by Spnnger-Verlag (Berlin/Heidelberg/New York) for sale in
the People's Republic of China only and not for export therefrom
Reprinted in China by Beijing World Publishing Corporation, 2003
987654321
ISBN 0-387-98934-X Spnnger-Verlag New York Berlin Heidelberg
SPIN 10745204
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