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arXiv · 1606.00814

A note on the non-Artinianness of top local cohomology modules

Tuğba Yıldırım
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Abstract

Let $R$ be a Noetherian ring, $I$ an ideal of $R$ and $M$ an $R$-module. In this article, we examine the question of whether an arbitrary top local cohomology module, $\operatorname{H}^{\operatorname{cd}(I,M)}_I(M)$, is Artinian, or not. Several results related to this question are obtained; in particular, we prove that over a Noetherian local unique factorization domain $R$ of dimension three, for a finitely generated faithful module $M$, a top local cohomology module is Artinian if and only if $\operatorname{cd}(I,M)= 3$.

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Tuğba Yıldırım. 2016-06-02. A note on the non-Artinianness of top local cohomology modules. https://arxiv.org/abs/1606.00814

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