## 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

## 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 $M$ 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.## References

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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: de@msri.org
**Craig Huneke**- Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
- MR Author ID: 89875
- Email: huneke@math.ukans.edu
**Bernd Ulrich**- Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
- MR Author ID: 175910
- Email: ulrich@math.purdue.edu
- 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: https://doi.org/10.1090/S0002-9939-02-06575-9
- MathSciNet review: 1937406