What is the Rees algebra of a module?

Authors:
David Eisenbud, Craig Huneke and Bernd Ulrich

Journal:
Proc. Amer. Math. Soc. **131** (2003), 701-708

MSC (2000):
Primary 13A30, 13B21; Secondary 13C12

DOI:
https://doi.org/10.1090/S0002-9939-02-06575-9

Published electronically:
September 17, 2002

MathSciNet review:
1937406

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Abstract | References | Similar Articles | Additional Information

Abstract: 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 may be computed in terms of a ``maximal'' map from to a free module as the image of the map induced by on symmetric algebras. We show that the analytic spread and reductions of can be determined from any embedding of 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

Email:
de@msri.org

**Craig Huneke**

Affiliation:
Department of Mathematics, University of Kansas, Lawrence, Kansas 66045

Email:
huneke@math.ukans.edu

**Bernd Ulrich**

Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907

Email:
ulrich@math.purdue.edu

DOI:
https://doi.org/10.1090/S0002-9939-02-06575-9

Keywords:
Rees algebra,
module,
integral dependence

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

Article copyright:
© Copyright 2002
American Mathematical Society