SOME RESULTS ON THE ARTINIAN COFINITE MODULES

Document Type : Original Manuscript

Author

Payame Noor University, P.O. Box 19395-3697, Tehran, Iran.

Abstract

Let $I$ be an ideal of a commutative Noetherian ring $R$ and $M$ be a non-zero Artinian $R$-module with support contained in $V(I)$. In this paper it is shown that $M$ is $I$-cofinite if and only if $Rad(I\widehat{R}^J+Ann_{\widehat{R}^J}M)=J\widehat{R}^J$, where $J:=\cap_{m\in Supp M}m$ and $\widehat{R}^J$ denotes the $J$-adic comletion of $R$.

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References

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Journal of Algebraic Systems
Volume 11, Issue 1
September 2023
Pages 97-103

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