University of Guilan Journal of Algebra and Related Topics 2345-3931 11 1 2023 06 01 On a question concerning the Cohen's theorem 49 53 6308 10.22124/jart.2022.22922.1432 EN S. S. Pourmortazavi Department of Mathematics, Guilan University, Rasht, Iran S. Keyvani Department of Mathematics, Bandar Anzali Branch, Islamic Azad University, Bandar Anzali Branch, Iran Journal Article 2022 09 14 Let $R$ be a commutative ring with identity, and let $M$ be an $R$-module.  The Cohen's theorem is the classic result that a ring is Noetherian if and only if its prime ideals are finitely generated. Parkash and Kour obtained a new version of Cohen's theorem for modules, which states that a finitely generated $R$-module $M$ is Noetherian if and only if for every prime ideal $p$ of $R$ with $Ann(M) \subseteq p$, there exists a finitely generated submodule $N$ of $M$ such that $pM \subseteq N \subseteq M(p)$, where $M(p) = \{x \in M | sx \in pM \,\,\textit{for some} \,\, s \in R \backslash p\}$. In this paper, we prove this result for some classes of modules.  https://jart.guilan.ac.ir/article_6308_acf6ba066d294be0dfbf50fc5dbe6e30.pdf