[PDF][PDF] On graded -classical prime submodules
K Al-Zoubi, S Alghueiri - Algebraic Structures and Their Applications, 2021 - as.yazd.ac.ir
Algebraic Structures and Their Applications, 2021•as.yazd.ac.ir
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 …
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 …
Let be a group with identity . Let be a -graded commutative ring with identity 1 and a graded -module. A proper graded submodule of is called a graded classical prime submodule if whenever and with , then either or . In this paper, we introduce the concept of graded -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 of is \textit{a graded }\textit{-classical prime submodule of \ } if whenever where and , then either or , where is the graded Jacobson radical.
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