On Cohen's theorem for Artinian modules

Xiaolei Zhang; Hwankoo Kim; Wei Qi

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arXiv · 2205.15586

On Cohen's theorem for Artinian modules

Xiaolei Zhang·Hwankoo Kim·Wei Qi

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Abstract

In this paper, we prove that a finitely embedded $R$-module $M$ is Artinian if and only if for every prime ideal $\mathfrak{p}$ of $R$ with $(0:_RM)\subseteq \mathfrak{p}$, there exists a submodule $N^\mathfrak{p}$ of $M$ such that $M/N^\mathfrak{p}$ is finitely embedded and $M[\mathfrak{p}]\subseteq N^\mathfrak{p}\subseteq (0:_M\mathfrak{p})$.

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Xiaolei Zhang, Hwankoo Kim, Wei Qi. 2022-05-31. On Cohen's theorem for Artinian modules. https://arxiv.org/abs/2205.15586

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