Finite Free Resolutions

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Overview

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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Product Details

  • ISBN-13: 9780521604871
  • Publisher: Cambridge University Press
  • Publication date: 6/3/2004
  • Series: Cambridge Tracts in Mathematics Series , #71
  • Pages: 284
  • Product dimensions: 5.43 (w) x 8.50 (h) x 0.63 (d)

Table of Contents

Preface; 1. Matrices and determinants; 2. Free modules; 3. The invariants of fitting and macrae; 4. Stability and finite free resolutions; 5. Latent non-zerodivisors; 6. Grade and finite free resolutions; 7. The multiplicative structure; Appendices; References; General index; Index of special symbols.

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