On the degree of Hilbert polynomials associated to the torsion functor

Authors:
Daniel Katz and Emanoil Theodorescu

Journal:
Proc. Amer. Math. Soc. **135** (2007), 3073-3082

MSC (2000):
Primary 13A30, 13D02, 13D07, 13D40

Published electronically:
May 14, 2007

MathSciNet review:
2322736

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a local, Noetherian ring and an ideal. A question of Kodiyalam asks whether for fixed , the polynomial giving the th Betti number of has degree equal to the analytic spread of minus one. Under mild conditions on , we show that the answer is positive in a number of cases, including when is divisible by or is an integrally closed -primary ideal.

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Additional Information

**Daniel Katz**

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

Email:
dlk@math.ku.edu

**Emanoil Theodorescu**

Affiliation:
Department of Mathematics, University of Missouri, Columbia, Missouri, 65211

Address at time of publication:
University of Iowa, Department of Actuarial Science and Statistics, 241 Schaeffer Hall, Iowa City, IA 52242

Email:
theodore@math.missouri.edu, emanoil.theodorescu@g.mail.com

DOI:
http://dx.doi.org/10.1090/S0002-9939-07-08879-X

Keywords:
Hilbert-Samuel polynomial,
torsion functor,
quasi-unmixed local ring

Received by editor(s):
December 14, 2005

Received by editor(s) in revised form:
June 28, 2006

Published electronically:
May 14, 2007

Communicated by:
Bernd Ulrich

Article copyright:
© Copyright 2007
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.