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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Free resolutions of parameter ideals for some rings with finite local cohomology
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by Hamidreza Rahmati PDF
Proc. Amer. Math. Soc. 136 (2008), 467-474 Request permission

Abstract:

Let $R$ be a $d$-dimensional local ring, with maximal ideal $\mathfrak {m}$, containing a field and let $x_1, \dots , x_d$ be a system of parameters for $R$. If $\operatorname {depth} R \geq d - 1$ and the local cohomology module $\operatorname {H}_{m}^{d-1}(R)$ is finitely generated, then there exists an integer $n$ such that the modules $R/(x_1^i,\dots ,x_d^i)$ have the same Betti numbers, for all $i\geq n$.
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Additional Information
  • Hamidreza Rahmati
  • Affiliation: Department of Mathematics, University of Nebraska, Lincoln, Nebraska 68588
  • Email: hrahmati@math.unl.edu
  • Received by editor(s): April 12, 2006
  • Received by editor(s) in revised form: January 12, 2007
  • Published electronically: November 3, 2007
  • Additional Notes: This research was partly supported by NSF grant DMS-0201904
  • Communicated by: Bernd Ulrich
  • © Copyright 2007 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 467-474
  • MSC (2000): Primary 13D02, 13D40; Secondary 13H10
  • DOI: https://doi.org/10.1090/S0002-9939-07-09127-7
  • MathSciNet review: 2358485