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Some results on the cofiniteness of local cohomology modules

Sohrab Sohrabi Laleh; Mir Yousef Sadeghi; Mahdi Hanifi Mostaghim — 2012

Czechoslovak Mathematical Journal

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...

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