On the degree of Hilbert polynomials associated to the torsion functor
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- by Daniel Katz and Emanoil Theodorescu PDF
- Proc. Amer. Math. Soc. 135 (2007), 3073-3082 Request permission
Abstract:
Let $R$ be a local, Noetherian ring and $I\subseteq R$ an ideal. A question of Kodiyalam asks whether for fixed $i > 0$, the polynomial giving the $i$th Betti number of $I^n$ has degree equal to the analytic spread of $I$ minus one. Under mild conditions on $R$, we show that the answer is positive in a number of cases, including when $I$ is divisible by $\mathfrak {m}$ or $I$ is an integrally closed $\mathfrak {m}$-primary ideal.References
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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
- 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
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 3073-3082
- MSC (2000): Primary 13A30, 13D02, 13D07, 13D40
- DOI: https://doi.org/10.1090/S0002-9939-07-08879-X
- MathSciNet review: 2322736