Journal of Algebraic Systems

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 $\widehat{R}^J$ ... Read More

MULTIPLICATION MODULES THAT ARE FINITELY GENERATED

Y. Tolooei

Volume 8, Issue 1 , September 2020, , Pages 1-5

https://doi.org/10.22044/jas.2019.8699.1421

Abstract

Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. An $R$-module $M$ is called a multiplication module if for every submodule $N$ of $M$ there exists an ideal $I$ of $R$ such that $N = IM$. It is shown that over a Noetherian domain $R$ with dim$(R)\leq 1$, multiplication modules ... Read More

Journal of Algebraic Systems

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Keywords = Noetherian ring

SOME RESULTS ON THE ARTINIAN COFINITE MODULES

Abstract

MULTIPLICATION MODULES THAT ARE FINITELY GENERATED

Abstract