SOME RESULTS ON THE ARTINIAN COFINITE MODULES | ||
| Journal of Algebraic Systems | ||
| دوره 11، شماره 1، آذر 2023، صفحه 97-103 اصل مقاله (128.32 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2022.11608.1588 | ||
| نویسنده | ||
| Gholamreza Pirmohammadi* | ||
| Payame Noor University, P.O. Box 19395-3697, Tehran, Iran. | ||
| چکیده | ||
| 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 $R$. | ||
| کلیدواژهها | ||
| Artinian module؛ attached prime ideal؛ cofinite module؛ Noetherian ring | ||
| مراجع | ||
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