论文标题
在$ gr $ - $ c $ - $ 2^{a} $ - 辅助子模型
On $Gr$-$C$-$2^{A}$-secondary submodules
论文作者
论文摘要
令$ω$为具有身份$ e $的集团，$γ$是$ω$的交换环和$ \ im $ a级$γ$ -Module。在本文中，我们介绍了$ gr $ - $ c $ - $ 2^{a} $ - 辅助子模型的概念，并调查了这一新等级的子模型的某些属性。 A non-zero graded submodule $S$ of $\Im$ is said to be a $gr$-$C$-$2^{A}$-secondary submodule if whenever $r,s \in h(Γ)$, $L$ is a graded submodule of $\Im$, and $rs\,S\subseteq L$, then either $r\,S\subseteq L$ or $ s \，s \ subseteq l $或$ rs \ in Gr（ann_γ（s））$。
Let $Ω$ be a group with identity $e$, $Γ$ be a $Ω$-graded commutative ring and $\Im$ a graded $Γ$-module. In this article, we introduce the concept of $gr$-$C$-$2^{A}$-secondary submodules and investigate some properties of this new class of graded submodules. A non-zero graded submodule $S$ of $\Im$ is said to be a $gr$-$C$-$2^{A}$-secondary submodule if whenever $r,s \in h(Γ)$, $L$ is a graded submodule of $\Im$, and $rs\,S\subseteq L$, then either $r\,S\subseteq L$ or $s\,S \subseteq L$ or $rs \in Gr(Ann_Γ(S))$.
