论文标题
在分级$ s $ - compultiplication模块
On graded $S$-comultiplication modules
论文作者
论文摘要
在本文中，我们介绍了分级$ s $ complicationation模块的概念。证明了有关分级$ s $ commultiplication模块的几个结果。我们表明，$ n $是分级$ s $ s $ second subsodule的分级$ s $ s $ -comultiplication $ r $ -module $ m $ If if if if ifry，并且仅当$ and_r（n）$是$ s $ s $ s-prime的理想的$ r $的理想，并且在s $中是否存在$ xn \ subseteq \ bar \ bar} $ x n $ S $。
In this paper, we introduce the concept of graded $S$-comultiplication modules. Several results concerning graded $S$-comultiplication modules are proved. We show that $N$ is a graded $S$-second submodule of a graded $S$-comultiplication $R$-module $M$ if and only if $Ann_R(N)$ is a graded $S$-prime ideal of $R$ and there exists $x\in S$ such that $xN\subseteq\bar{x}N$ for every $\bar{x}\in S$.
