论文标题
在Cohen的Artinian模块定理上
On Cohen's theorem for Artinian modules
论文作者
论文摘要
在本文中，我们证明了一个有限嵌入的$ r $ -module $ m $是artinian，并且仅当每个主要的理想$ \ mathfrak {p} $ a $ r $带有$（0：_rm）\ supseteq \ supseteq \ mathfrak {p} $时，就会存在subpodule $ n^^\ mathfrak $ $ $ $ $ $ $} $ m/n^\ mathfrak {p} $有限嵌入，$ m [\ mathfrak {p}] \ subseteq n^\ mathfrak {p} \ subseteq（0：_m \ mathfrak {p}）$。
In this paper, we prove that a finitely embedded $R$-module $M$ is Artinian if and only if for every prime ideal $\mathfrak{p}$ of $R$ with $(0:_RM)\subseteq \mathfrak{p}$, there exists a submodule $N^\mathfrak{p}$ of $M$ such that $M/N^\mathfrak{p}$ is finitely embedded and $M[\mathfrak{p}]\subseteq N^\mathfrak{p}\subseteq (0:_M\mathfrak{p})$.
