论文标题
在弱S主要子模型上
On Weakly S-primary Submodules
论文作者
论文摘要
令$ r $为具有非零身份的交换戒指，$ s $是$ r $的多个封闭子集，$ m $是Unital $ r $ $ module。在本文中，我们将$ n $ of $ m $定义为$（n：_ {r} m）\ cap s = \ emptySet $，如果存在$ s \ in s $ in s $ s $ s $ s $ s $ primary，则只要$ a \ in r $ in $ $ a $ and $ m \ in m $ in m $ n n $ n $ \ neq in n $ \ in n n $， $ sa \ in \ sqrt {（n：_ {r} m）} $或$ sm \ in n $。我们介绍了此概念的各种属性和特征（尤其是在有限生成的忠实乘法模块中）。此外，研究了该结构在模块同态，本地化，商模块，笛卡尔产品和理想化下的行为。最后，我们确定了一些条件，在这些条件下，沿理想的融合模块的两种子模块是薄弱的$ s $ primary。
Let $R$ be a commutative ring with a non-zero identity, $S$ be a multiplicatively closed subset of $R$ and $M$ be a unital $R$-module. In this paper, we define a submodule $N$ of $M$ with $(N:_{R}M)\cap S=\emptyset$ to be weakly $S$-primary if there exists $s\in S$ such that whenever $a\in R$ and $m\in M$ with $0\neq am\in N$, then either $sa\in\sqrt{(N:_{R}M)}$ or $sm\in N$. We present various properties and characterizations of this concept (especially in finitely generated faithful multiplication modules). Moreover, the behavior of this structure under module homomorphisms, localizations, quotient modules, cartesian product and idealizations is investigated. Finally, we determine some conditions under which two kinds of submodules of the amalgamation module along an ideal are weakly $S$-primary.
