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Introduction to Some Methods of Algebraic \(K\)-Theory
H. Bass
A co-publication of the AMS and CBMS.

CBMS Regional Conference Series in Mathematics
1974; 68 pp; softcover
Number: 20
Reprint/Revision History:
fifth printing 2000
ISBN-10: 0-8218-1670-5
ISBN-13: 978-0-8218-1670-7
List Price: US$30
Member Price: US$24
All Individuals: US$24
Order Code: CBMS/20
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Table of Contents

Part I. Introduction
  • Elementary matrices
  • Stability
  • \(K_1(A[t])\) and unipotents
  • Grothendieck and Whitehead groups of categories with exact sequences
  • A Grothendieck style definition of \(K_1(A)\)
  • Homology, mapping cones, and Euler characteristics
  • Resolution theorems
  • Projective resolutions and regular rings
  • Hilbert's syzygy theorem
  • Appendix 1
Part II. Localisation, divissage and applications
  • The localisation sequence
  • Categories of nilpotent endomorphisms
  • \(K_1(A[t,t^-1])\)
  • Devissage
  • Some calculations with the localisation sequence and \(K_1\)-Laurent theorem
  • Computations with the Mayer-Vietoris sequence
  • References
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