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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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Finiteness properties of local cohomology modules for $\mathfrak a$-minimax modules
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by Jafar Azami, Reza Naghipour and Bahram Vakili PDF
Proc. Amer. Math. Soc. 137 (2009), 439-448 Request permission

Abstract:

Let $R$ be a commutative Noetherian ring and $\mathfrak a$ an ideal of $R$. In this paper we introduce the concept of $\mathfrak a$-minimax $R$-modules, and it is shown that if $M$ is an $\mathfrak a$-minimax $R$-module and $t$ a non-negative integer such that $\textrm {H}_\mathfrak a^i(M)$ is $\mathfrak a$-minimax for all $i<t$, then for any $\mathfrak a$-minimax submodule $N$ of $\textrm {H}_\mathfrak a^t(M)$, the $R$-module $\textrm {Hom}_R(R/\mathfrak a,\textrm {H}_\mathfrak a^t(M)/N)$ is $\mathfrak a$-minimax. As a consequence, it follows that the Goldie dimension of $\textrm {H}_\mathfrak a^t(M)/N$ is finite, and so the associated primes of $\textrm {H}_\mathfrak a^t(M)/N$ are finite. This generalizes the main result of Brodmann and Lashgari (2000).
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Additional Information
  • Jafar Azami
  • Affiliation: Department of Mathematics, University of Tabriz, Tabriz 51666-16471, Iran – and – Department of Mathematics, Mohaghegh Ardabily University, Ardabil, Iran
  • Email: azami@tabrizu.ac.ir
  • Reza Naghipour
  • Affiliation: Department of Mathematics, University of Tabriz, Tabriz 51666-16471, Iran – and – School of Mathematics, Institute for Studies in Theoretical Physics and Mathematics (IPM), P.O. Box 19395-5746, Tehran, Iran
  • Email: naghipour@ipm.ir, naghipour@tabrizu.ac.ir
  • Bahram Vakili
  • Affiliation: Department of Mathematics, Science and Research Branch, Islamic Azad University, P.O. Box 14515-775, Tehran, Iran – and – Department of Mathematics, Shabestar Islamic Azad University, Shabestar, Iran
  • Email: bvakil@iaushab.ac.ir
  • Received by editor(s): October 3, 2007
  • Received by editor(s) in revised form: January 18, 2008
  • Published electronically: August 25, 2008
  • Additional Notes: The research of the second author was supported in part by a grant from IPM (No. 86130031)
  • Communicated by: Bernd Ulrich
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 439-448
  • MSC (2000): Primary 13D45, 14B15, 13E05
  • DOI: https://doi.org/10.1090/S0002-9939-08-09530-0
  • MathSciNet review: 2448562