Journal of Algebraic Systems

Let R be a commutative Noetherian ring, I, J be ideals of R such thatJ ⊆ I, and M be a finitely generated R-module. In this paper, we prove that theinvariants AJI(M) := inf{i ∈ N0 | JtHiI (M) is not Artinian for all t ∈ N0} and inf{i ∈N0 | JtHiI (M) is not minimax for all t ∈ ... Read More

SOME RESULTS ON THE ARTINIAN COFINITE MODULES

Gholamreza Pirmohammadi

Volume 11, Issue 1 , September 2023, , Pages 97-103

https://doi.org/10.22044/jas.2022.11608.1588

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

Journal of Algebraic Systems

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Keywords = Artinian module

ON THE MINIMAXNESS AND ARTINIANNESS DIMENSIONS

Abstract

SOME RESULTS ON THE ARTINIAN COFINITE MODULES

Abstract