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Other titles in the Cambridge Tracts in Mathematics series:
Finite Free Resolutionsby D. G. Northcott
Synopses & ReviewsPublisher Comments: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 selfcontained 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.
Synopsis:This Cambridge Tract attempts to give a genuinely selfcontained and elementary presentation of the basic theory of finite free resolutions, and to provide a sound foundation for further study. The text contains a substantial number of exercises to test the reader's understanding of the subject. Each chapter ends with the solutions to the exercises contained in it.
Synopsis:A genuinely selfcontained and elementary presentation of the basic theory of finite free resolutions.
Table of ContentsPreface; 1. Matrices and determinants; 2. Free modules; 3. The invariants of fitting and macrae; 4. Stability and finite free resolutions; 5. Latent nonzerodivisors; 6. Grade and finite free resolutions; 7. The multiplicative structure; Appendices; References; General index; Index of special symbols.
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