@article { author = {Al-Zoubi, khaldoun and Alghueiri, Shatha}, title = {On graded $J_{gr}$-classical prime submodules}, journal = {Algebraic Structures and Their Applications}, volume = {8}, number = {2}, pages = {195-201}, year = {2021}, publisher = {Yazd University}, issn = {2382-9761}, eissn = {2423-3447}, doi = {10.22034/as.2021.2121}, abstract = {Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative ring with identity 1 and $M$ a graded $R$-module. A proper graded submodule $C$ of $M$ is called a graded classical prime submodule if whenever $r,s\in h(R)$ and $m\in h(M)$ with $rsm\in C$, then either $rm\in C$ or $sm\in C$. In this paper, we introduce the concept of graded $J_{gr}$-classical prime submodule as a new generalization of graded classical submodule and we give some results concerning such graded modules. We say that a proper graded submodule $N$ of $M$ is \textit{a graded }$J_{gr}$\textit{-classical prime submodule of \ }$M$ if whenever $rsm\in N$ where $r,s\in h(R)$ and $m\in h(M)$, then either $rm\in N+J_{gr}(M)$ or $sm\in N+J_{gr}(M)$, where $J_{gr}(M)$ is the graded Jacobson radical.}, keywords = {Graded classical prime submodule,Graded $J_{gr}$-classical prime submodule,Graded prime}, url = {https://as.yazd.ac.ir/article_2121.html}, eprint = {https://as.yazd.ac.ir/article_2121_5bd6ab9b64e4a6a1a3c24c741a28c88a.pdf} }