论文标题
在两个版本的Cohen的模块定理上
On two versions of Cohen's theorem for modules
论文作者
论文摘要
Parkash和Kour获得了Noetherian模块的Cohen定理的新版本，该定理指出，当且仅当每个Prime of Ann $（m）$（m）\ Mathfrak \ subseteq \ mathfrak {p} $ pribity n exist a Exists a Exists A Exists A Ann $（m） $ m $ $ n^\ mathfrak {p} $ $ \ mathfrak {p} m \ subseteq n^\ mathfrak {p} \ subseteq m（\ mathfrak {p}）$ $ s \ in r \ setMinus \ mathfrak {p} \} $。在本文中，我们将Cohen定理的Parkash和Kour版本概括为Noetherian模块的，以$ s $ -noetherian模块和$ W $ -W $ -Noetherian模块。
Parkash and Kour obtained a new version of Cohen's theorem for Noetherian modules, which states that a finitely generated $R$-module $M$ is Noetherian if and only if for every prime ideal $\mathfrak{p}$ of $R$ with Ann$(M)\subseteq \mathfrak{p}$, there exists a finitely generated submodule $N^\mathfrak{p}$ of $M$ such that $\mathfrak{p} M\subseteq N^\mathfrak{p}\subseteq M(\mathfrak{p})$, where $M(\mathfrak{p})=\{x\in M\mid sx\in \mathfrak{p} M $ for some $s\in R \setminus \mathfrak{p} \}$. In this paper, we generalize the Parkash and Kour version of Cohen's theorem for Noetherian modules to those for $S$-Noetherian modules and $w$-Noetherian modules.
