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  3. Finite Free Resolutions
  • Cited by 129
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    • Publisher:
      Cambridge University Press
      Publication date:
      December 2009
      August 1976
      ISBN:
      9780511565892
      9780521604871
      DOI:
      https://doi.org/10.1017/CBO9780511565892
      Dimensions:
      Weight & Pages:
      Dimensions:
      (216 x 138 mm)
      Weight & Pages:
      0.36kg, 284 Pages
      • Subjects:
      Mathematics (general), Mathematics, Algebra
      Series:
      Cambridge Tracts in Mathematics (71)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Algebra
    Series:
    Cambridge Tracts in Mathematics (71)
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    Book description

    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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