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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the cofiniteness of local cohomology modules


Authors: Kamal Bahmanpour and Reza Naghipour
Journal: Proc. Amer. Math. Soc. 136 (2008), 2359-2363
MSC (2000): Primary 13D45, 14B15, 13E05
Published electronically: March 4, 2008
MathSciNet review: 2390502
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Abstract: In this note we show that if $ I$ is an ideal of a Noetherian ring $ R$ and $ M$ is a finitely generated $ R$-module, then for any minimax submodule $ N$ of $ H^{t}_{I}(M)$ the $ R$-module $ {\rm Hom}_{R}(R/I,H_{I}^{t}(M)/N)$ is finitely generated, whenever the modules $ H_{I}^{0}(M),\, H_{I}^{1}(M),..., \,H_{I}^{t-1}(M)$ are minimax. As a consequence, it follows that the associated primes of $ H^{t}_{I}(M)/N$ are finite. This generalizes the main result of Brodmann and Lashgari (2000).


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Additional Information

Kamal Bahmanpour
Affiliation: Department of Mathematics, University of Tabriz, Tabriz, Iran – and – Department of Mathematics, Islamic Azad University-Ardebil Branch, P.O. Box 5614633167, Ardebil, Iran
Email: bahmanpour@tabrizu.ac.ir

Reza Naghipour
Affiliation: Department of Mathematics, University of Tabriz, Tabriz, 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

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09260-5
PII: S 0002-9939(08)09260-5
Keywords: Local cohomology, cofinite module, minimax module, associated primes.
Received by editor(s): February 27, 2007
Received by editor(s) in revised form: May 17, 2007
Published electronically: March 4, 2008
Additional Notes: The research of the second author has been in part supported by a grant from IPM (No. 85130042)
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.