Autor: |
Alnimer, Malak, Al-Zoubi, Khaldoun, Al-Dolat, Mohammed |
Předmět: |
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Zdroj: |
AIMS Mathematics (2473-6988); 2024, Vol. 9 Issue 5, p12315-12322, 8p |
Abstrakt: |
Let Γ be a group, A be a Γ-graded commutative ring with unity 1, and D a graded A-module. In this paper, we introduce the concept of graded weakly Jgr-semiprime submodules as a generalization of graded weakly semiprime submodules. We study several results concerning of graded weakly Jgr-semiprime submodules. For example, we give a characterization of graded weakly Jgr-semiprime submodules. Also, we find some relations between graded weakly Jgr-semiprime submodules and graded weakly semiprime submodules. In addition, the necessary and sufficient condition for graded submodules to be graded weakly Jgr-semiprime submodules are investigated. A proper graded submodule U of D is said to be a graded weakly Jgr-semiprime submodule of D if whenever rg ∈ h(A); mh ∈ h(D) and n ∈ Z+ with 0 ≠ rngmh ∈ U, then rgmh ∈ U + Jgr(D), where Jgr(D) is the graded Jacobson radical of D. [ABSTRACT FROM AUTHOR] |
Databáze: |
Complementary Index |
Externí odkaz: |
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