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• W1481781336 abstract "Let $R$ be a commutative noetherian ring, $I,J$ be two ideals of $R$, $M$ be an $R$-module, and $mathcal{S}$ be a Serre class of $R$-modules. A positive answer to the Huneke$^,$s conjecture is given for a noetherian ring $R$ and minimax $R$-module $M$ of krull dimension less than 3, with respect to $mathcal{S}$. There are some results on cofiniteness and artinianness of local cohomology modules with respect to a pair of ideals. For a ZD-module $M$ of finite krull dimension and an integer $ninmathbb{N}$, if $lc^{i}_{I,J}(M)inmathcal{S}$ for all $i>n$, then $lc^{i}_{I,J}(M)/fa^{j}lc^{i}_{I,J}(M)inmathcal{S}$ for any $faintilde{W}(I,J)$, all $igeq n$, and all $jgeq0$. By introducing the concept of Seree cohomological dimension of $M$ with respect to $(I,J)$, for an integer $rinmathbb{N}_0$, $lc^{j}_{I,J}(R)inmathcal{S}$ for all $j>r$ iff $lc^{j}_{I,J}(M)inmathcal{S}$ for all $j>r$ and any finite $R$-module $M$." @default.
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• W1481781336 date "2012-11-18" @default.
• W1481781336 modified "2023-09-27" @default.
• W1481781336 title "Upper bounds, cofiniteness, and artinianness of local cohomology modules defined by a pair of ideals" @default.
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