Gholamreza Pirmohammadi: Attached primes of top local cohomology modules, 149-157

Abstract:

Let ${\operatorname{\frak a}}$ be an ideal of a Noetherian complete local ring $(R,{\operatorname{\frak m}})$ and $M$ be a finitely generated $R$-module with ${\operatorname{cd}}({\operatorname{\frak a}},M)=c\geq 1$. Assume that the $R$-module $H^c_{{\operatorname{\frak a}}}(M)$ is Artinian. In this paper, it is shown that

$${\operatorname{Att}}_R H^c_{{\operatorname{\frak a}}}(M)\subseteq... ...torname{Ann}}_R H^{c}_{{\operatorname{\frak a}}}(R/{\operatorname{\frak p}})\}.$$

Key Words: Artinian module, attached prime ideal, cofinite module, local cohomology, Noetherian ring.

2020 Mathematics Subject Classification: Primary 13D45; Secondary 14B15, 13E05.

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