Finite Free Resolutions
Finite Free Resolutions (Cambridge Tracts in Mathematics)
D. G. Northcott, B. Bollobas (Series Editor), W. Fulton (Series Editor), A. Katok (Series Editor), F. Kirwan (Series Editor), P. Sarnak (Series Editor)
Publisher: Cambridge University Press
ISBN: 0521604877
Edition: Paperback; 2004-06-03
Summary:
An important part of homological algebra deals with modules
possessing projective resolutions of finite length. This goes back to
Hilbert's famous theorem on syzygies through, in the earlier theory,
free modules with finite bases were used rather than projective
modules. The introduction of a wider class of resolutions led to a
theory rich in results, but in the process certain special properties
of finite free resolutions were overlooked. D. A. Buchsbaum and D.
Eisenbud have shown that finite free resolutions have a fascinating
structure theory. This has revived interest in the simpler kind of
resolution and caused the subject to develop rapidly. This Cambridge
Tract attempts to give a genuinely self-contained and elementary
presentation of the basic theory, and to provide a sound foundation
for further study. The text contains a substantial number of
exercises. These enable the reader to test his understanding and they
allow the subject to be developed more rapidly. Each chapter ends
with the solutions to the exercises contained in it.
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