Some results on the cofiniteness of local cohomology modules |
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| Authors: | Sohrab Sohrabi Laleh Mir Yousef Sadeghi Mahdi Hanifi Mostaghim |
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| Institution: | 1. Department of Mathematics, Islamic Azad University, Shabestar Branch, Shabestar, Iran
2. Tehran Graduate Center, Payam-e-Noor University, Tehran, Iran
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| Abstract: | Let R be a commutative Noetherian ring, a an ideal of R, M an R-module and t a non-negative integer. In this paper we show that the class of minimax modules includes the class of AF modules. The main result is that if the R-module Ext
R
t
(R/a,M) is finite (finitely generated), H
a
i
(M) is a-cofinite for all i < t and H
a
t
(M) is minimax then H
a
t
(M) is a-cofinite. As a consequence we show that if M and N are finite R-modules and H
a
i
(N) is minimax for all i < t then the set of associated prime ideals of the generalized local cohomology module H
a
t
(M,N) is finite. |
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| Keywords: | |
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