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© 1995

Homology

Book

Part of the Classics in Mathematics book series (volume 114)

Table of contents

  1. Front Matter
    Pages I-X
  2. Saunders Mac Lane
    Pages 1-8
  3. Saunders Mac Lane
    Pages 8-34
  4. Saunders Mac Lane
    Pages 34-63
  5. Saunders Mac Lane
    Pages 63-103
  6. Saunders Mac Lane
    Pages 103-138
  7. Saunders Mac Lane
    Pages 138-172
  8. Saunders Mac Lane
    Pages 173-200
  9. Saunders Mac Lane
    Pages 200-220
  10. Saunders Mac Lane
    Pages 220-248
  11. Saunders Mac Lane
    Pages 248-279
  12. Saunders Mac Lane
    Pages 280-318
  13. Saunders Mac Lane
    Pages 318-358
  14. Saunders Mac Lane
    Pages 358-403
  15. Back Matter
    Pages 404-422

About this book

Introduction

In presenting this treatment of homological algebra, it is a pleasure to acknowledge the help and encouragement which I have had from all sides. Homological algebra arose from many sources in algebra and topology. Decisive examples came from the study of group extensions and their factor sets, a subject I learned in joint work with OTTO SCHIL­ LING. A further development of homological ideas, with a view to their topological applications, came in my long collaboration with SAMUEL ElLENBERG; to both collaborators, especial thanks. For many years the Air Force Office of Scientific Research supported my research projects on various subjects now summarized here; it is a pleasure to acknowledge their lively understanding of basic science. Both REINHOLD BAER and JOSEF SCHMID read and commented on my entire manuscript; their advice has led to many improvements. ANDERS KOCK and JACQUES RIGUET have read the entire galley proof and caught many slips and obscurities. Among the others whose sug­ gestions have served me well, I note FRANK ADAMS, LOUIS AUSLANDER, WILFRED COCKCROFT, ALBRECHT DOLD, GEOFFREY HORROCKS, FRIED­ RICH KASCH, JOHANN LEICHT, ARUNAS LIULEVICIUS, JOHN MOORE, DIE­ TER PUPPE, JOSEPH YAO, and a number of my current students at the University of Chicago - not to m~ntion the auditors of my lectures at Chicago, Heidelberg, Bonn, Frankfurt, and Aarhus. My wife, DOROTHY, has cheerfully typed more versions of more chapters than she would like to count. Messrs.

Keywords

Abelian group Factor algebra auditor cohomology collaboration commutative ring development group homological algebra homology proof sets topology university

Authors and affiliations

  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA

About the authors

Biography of Saunders Mac Lane

Saunders Mac Lane was born on August 4, 1909 in Connecticut. He studied at Yale University and then at the University of Chicago and at Göttingen, where he received the D.Phil. in 1934. He has tought at Harvard, Cornell and the University of Chicago.

Mac Lane's initial research was in logic and in algebraic number theory (valuation theory). With Samuel Eilenberg he published fifteen papers on algebraic topology. A number of them involved the initial steps in the cohomology of groups and in other aspects of homological algebra - as well as the discovery of category theory. His famous and undergraduate textbook Survey of modern algebra, written jointly with G. Birkhoff, has remained in print for over 50 years. Mac Lane is also the author of several other highly successful books.

Bibliographic information

  • Book Title Homology
  • Authors Saunders MacLane
  • Series Title Classics in Mathematics
  • DOI https://doi.org/10.1007/978-3-642-62029-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 1995
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-03823-8
  • Softcover ISBN 978-3-540-58662-3
  • eBook ISBN 978-3-642-62029-4
  • Series ISSN 0072-7830
  • Edition Number 1
  • Number of Pages X, 422
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Additional Information Originally published as volume 114 in the series: Grundlehren der mathematischen Wissenschaften
  • Topics Category Theory, Homological Algebra
  • Buy this book on publisher's site