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On the cofiniteness of local cohomology modules

Authors:	Kamal Bahmanpour Reza Naghipour

Institution:	Department of Mathematics, University of Tabriz, Tabriz, Iran -- and -- Department of Mathematics, Islamic Azad University-Ardebil Branch, P.O. Box 5614633167, Ardebil, Iran ; 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

Abstract:	In this note we show that if is an ideal of a Noetherian ring and is a finitely generated -module, then for any minimax submodule of $H^{t}_{I}(M)$ the -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).

Keywords:	Local cohomology cofinite module minimax module associated primes

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