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Cofiniteness of generalized local cohomology modules | Synapse

May 30, 2024Journal of Algebra and Its Applications1 citations

Cofiniteness of generalized local cohomology modules

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JSJingwen Shen YXYang Xiaoyan

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Abstract

Let Formula: see text be an ideal of a commutative noetherian ring Formula: see text and Formula: see text two Formula: see text-modules with Formula: see text finitely generated. It is shown that if either Formula: see text is an Formula: see text-cofinite module of dimension Formula: see text for all Formula: see text, or Formula: see text is a principal ideal and Formula: see text is finitely generated for all Formula: see text, or Formula: see text is finitely generated and Formula: see text for all Formula: see text, then the Formula: see text-module Formula: see text is Formula: see text-cofinite for all Formula: see text.

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Cite This Study

Shen et al. (2024) studied this question.

synapsesocial.com/papers/68e67a9ab6db643587604b3a https://doi.org/10.1142/s0219498825503153

Also Consider

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1On the cofiniteness of generalized local cohomology modules2015 · 11 citations
2On the cofiniteness of generalized local cohomology modules with respect to the class of modules in dimension less than a fixed integer2021 · 1 citations
3On Vanishing and Cofiniteness of Generalized Local Cohomology Modules2009 · 25 citations
4On the generalized local cohomology and its duality1978 · 108 citations
5Cofiniteness of Local Cohomology Modules for Principal Ideals1998 · 56 citations