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).References
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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