On the Category of Weakly Laskerian Cofinite Modules

Abstract

Let $R$ denote a commutative Noetherian (not necessarily local) ring and $I$ be an ideal of $R$. The main purpose of this note is to show that the category $\mathscr{WL}(R, I)_{\it cof}$ of $I$-cofinite weakly Laskerian $R$-modules forms an Abelian subcategory of the category of all $R$-modules.