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- W1619437387 abstract "Let $R$ denote a commutative Noetherian (not necessarily local) ring, $M$ an arbitrary $R$-module and $I$ an ideal of $R$ of dimension one. It is shown that the $R$-module $Ext^i_R(R/I,M)$ is finitely generated (resp. weakly Laskerian) for all $ileq {rm cd}(I,M)+1$ if and only if the local cohomology module $H^i_I(M)$ is $I$-cofinite (resp. $I$-weakly cofinite) for all $i$. Also, we show that when $I$ is an arbitrary ideal and $M$ is finitely generated module such that the $R$-module $H^i_I(M)$ is weakly Laskerian for all $ileq t-1$, then $H^i_I(M)$ is $I$-cofinite for all $ileq t-1$ and for any minimax submodule $K$ of $H^{t}_I(M)$, the $R$-modules $Hom_R(R/I, H^{t}_I(M)/K)$ and $Ext^{1}_R(R/I, H^{t}_I(M)/K)$ are finitely generated, where $t$ is a non-negative integer. This generalizes the main result of Bahmanpour-Naghipour cite{BN} and Brodmann and Lashgari cite{BL}." @default.
- W1619437387 created "2016-06-24" @default.
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- W1619437387 date "2013-08-28" @default.
- W1619437387 modified "2023-09-27" @default.
- W1619437387 title "Cofiniteness of local cohomology modules for ideals of dimension one" @default.
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