Geodesic
Some results on top local cohomology modules with respect to a pair of ideals
Mathematica Bohemica, Tome 145 (2020) no. 4, pp. 377-386
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Let $I$ and $J$ be ideals of a Noetherian local ring $(R,\mathfrak m)$ and let $M$ be a nonzero finitely generated $R$-module. We study the relation between the vanishing of $H_{I,J}^{\dim M}(M)$ and the comparison of certain ideal topologies. Also, we characterize when the integral closure of an ideal relative to the Noetherian $R$-module $M/JM$ is equal to its integral closure relative to the Artinian $R$-module $H_{I,J}^{\dim M}(M)$.
Let $I$ and $J$ be ideals of a Noetherian local ring $(R,\mathfrak m)$ and let $M$ be a nonzero finitely generated $R$-module. We study the relation between the vanishing of $H_{I,J}^{\dim M}(M)$ and the comparison of certain ideal topologies. Also, we characterize when the integral closure of an ideal relative to the Noetherian $R$-module $M/JM$ is equal to its integral closure relative to the Artinian $R$-module $H_{I,J}^{\dim M}(M)$.
DOI : 10.21136/MB.2019.0124-18
Classification : 13B22, 13D45, 13E05
Keywords: Artinian module; integral closure; local cohomology; quasi-unmixed module 
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Jahandoust, Saeed; Naghipour, Reza. Some results on top local cohomology modules with respect to a pair of ideals. Mathematica Bohemica, Tome 145 (2020) no. 4, pp. 377-386. doi: 10.21136/MB.2019.0124-18

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