论文标题
S-Prime和S Weakly Prime子模型
S-prime and S-weakly prime submodules
论文作者
论文摘要
在这项研究中，所有环具有非零身份的交换性，所有模块都被认为是Unital的。令$ m $为左$ r $ - 模块。如果$ 0_ {m} \ neq f（m）\ in n $ in n $ in n $ n $或$ f（m）\ subseteq n，$ f（m）\ subseteq n，$ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ f \ subseteq n，$ n $ in $ f \ in $ f \ in s = end（m）$和m $。获得了一些有关$ s $ prime和$ s $ weakly Prime subsodules的结果。然后，我们研究$ s $ prime和$ s $ weakly prime subplication模块。同样，对于$ r $ -Modules $ m_ {1} $和$ m_ {2}，$我们检查$ s $ - prime和$ s $ - $ s-neakly prime subsodules的$ m = m_ {1} \ times m_ {2}，$ $ s_ {2} = end（m_ {2}）$。
In this study, all rings are commutative with non-zero identity and all modules are considered to be unital. Let $M$ be a left $R$-module. A proper submodule $N$ of $M$ is called an $S$-$weakly$ $prime$ submodule if $0_{M}\neq f(m)\in N$ implies that either $m\in N$ or $f(M)\subseteq N,$ where $f\in S=End(M)$ and $m\in M$. Some results concerning $S$-prime and $S$-weakly prime submodules are obtained. Then we study $S$-prime and $S$-weakly prime submodules of multiplication modules. Also for $R$-modules $M_{1}$ and $M_{2},$ we examine $S$-prime and $S$-weakly prime submodules of $M=M_{1}\times M_{2},$ where $S=S_{1}\times S_{2},$ $S_{1}=End(M_{1})$ and $S_{2}=End(M_{2})$.
