On Graded Weakly Jgr-classical Prime Submodules
Malak Alnimer1,∗ , Khaldoun Al-Zoubi1
1Department of Mathematics and Statistics, Jordan University of Science and Technology, P.O.Box 3030,
Irbid 22110, Jordan
Emails: mfalnimer21@sci.just.edu.jo; kfzoubi@just.edu.jo
Abstract
Let 0 be a group, Υ be a 0-graded commutative ring with unity 1 and M a graded Υ-module. Our goal
in this paper, introducing the concept of graded weakly Jgr -classical prime submodule as a generalization
of graded weakly classical prime submodule and offering several results pertinent of graded weakly Jgr -
classical prime submodules. For instance, we give characterizations of graded weakly Jgr -classical prime
submodule. Also, we give some restrictions for graded submodule to be a graded weakly Jgr -classical prime
submodule. A proper graded submodule V of M is said to be a graded weakly Jgr -classical prime submodule
of M if, whenever 0̸ = abx ∈ V where a, b ∈ h(Υ) and x ∈ h(M), then either ax ∈ V + Jgr (M) or
bx ∈ V + Jgr (M), The symbol Jgr (M) indicates the graded Jacobson radical of Υ-module M.
Keywords: Graded weakly Jgr -classical prime submodule; Graded Jgr -classical prime submodule; Graded
weakly classical prime submodule; Graded classical prime submodule