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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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What is the Rees algebra of a module?
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by David Eisenbud, Craig Huneke and Bernd Ulrich PDF
Proc. Amer. Math. Soc. 131 (2003), 701-708 Request permission


In this paper we show that the Rees algebra can be made into a functor on modules over a ring in a way that extends its classical definition for ideals. The Rees algebra of a module $M$ may be computed in terms of a “maximal” map $f$ from $M$ to a free module as the image of the map induced by $f$ on symmetric algebras. We show that the analytic spread and reductions of $M$ can be determined from any embedding of $M$ into a free module, and in characteristic 0—but not in positive characteristic!—the Rees algebra itself can be computed from any such embedding.
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Additional Information
  • David Eisenbud
  • Affiliation: Mathematical Sciences Research Institute, 1000 Centennial Dr., Berkeley, California 94720
  • MR Author ID: 62330
  • ORCID: 0000-0002-5418-5579
  • Email:
  • Craig Huneke
  • Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
  • MR Author ID: 89875
  • Email:
  • Bernd Ulrich
  • Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
  • MR Author ID: 175910
  • Email:
  • Received by editor(s): May 2, 2001
  • Received by editor(s) in revised form: October 19, 2001
  • Published electronically: September 17, 2002
  • Additional Notes: All three authors were partially supported by the NSF
  • Communicated by: Wolmer V. Vasconcelos
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 701-708
  • MSC (2000): Primary 13A30, 13B21; Secondary 13C12
  • DOI:
  • MathSciNet review: 1937406