Let $G$ be an abelian group with identity $e$. Let $R$ be a $G$-graded commutative ring with identity and $M$ a graded $R$-module. In this paper, we introduce the concept of graded 2-absorbing $I_{e}$-prime submodule as a generalization of a graded 2-absorbing prime submodule for $\ I=\oplus _{g\in G}I_{g}$ a fixed graded ideal of $R$. We give a number of results concerning these classes of graded submodules and their homogeneous components. A proper graded submodule $N$ of $M$ is said to be a graded 2-absorbing $I_{e}$-prime submodule of $M$ if whenever $% r_{h},s_{\lambda }\in h(R)$ and $m_{\alpha }\in h(M)$ with $r_{h}s_{\lambda }m_{\alpha }\in N\backslash I_{e}N$, implies either $r_{h}s_{\lambda }\in (N:_{R}M)$ or $r_{h}m_{\alpha }\in N$ or $s_{\lambda }m_{\alpha }\in N.$

中文翻译：

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关于梯度交换环上梯度模块的2吸收的$ I_ {e} $-素数子模块

假设$ G $为身份为$ e $的阿贝尔群。假设$ R $是具有身份的$ G $等级的交换环，而$ M $是等级$ R $-模块。在本文中，我们引入了渐进2吸收的$ I_ {e} $-prime子模块的概念，作为对$ \ I = \ oplus _ {g \ in G} I_ {g } $固定等级理想$ R $。我们给出了有关这些类别的分级子模块及其同类组件的许多结果。如果每当$％r_ {h}，s _ {\ lambda} \ h时，则将适当的$ M $的分级子模块$ N $称为$ M $的分级2吸收$ I_ {e} $-素数子模块。 （R）$和$ m _ {\ alpha} \在h（M）$中，带有$ r_ {h} s _ {\ lambda} m _ {\ alpha} \在N \反斜杠I_ {e} N $中，表示$ r_ {h} s _ {\ lambda} \ in（N：_ {R} M）$或$ r_ {h} m _ {\ alpha} \ in N $或$ s _ {\ lambda} m _ {\ alpha} \ in N $