On graded Pe-Jgr-primary submodules

Alghueiri, Shatha; Al-Zoubi, Khaldoun

doi:10.47974/JDMSC-2613

Open Access Research Article

On graded Pe-Jgr-primary submodules

^*Shatha AlghueiriCorresponding authorsoalghueiri@just.edu.joDepartment of Mathematics and StatisticsFaculty of Science and ArtsJordan University of Science and TechnologyIrbid, P. O. Box 3030, 22110, JordanView full profile → , Khaldoun Al-Zoubikfzoubi@just.edu.joDepartment of Mathematics and StatisticsFaculty of Science and ArtsJordan University of Science and TechnologyIrbid, P. O. Box 3030, 22110, Jordan0000-0001-6082-4480View full profile →

* Corresponding author · click or hover a name for details

pp. 1855–1862Vol. 29Issue 4April 2026DOI: 10.47974/JDMSC-2613 Crossmark XML

Received:: 01 May 2025
Published Online:: 24 Mar 2026
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-2613
Pages:: 1855–1862

Abstract

This study investigates the concept of gr-Pe-Jgr-PrySups as an extension of gr-Jgr-PrySub within the framework of Ω-graded commutative rings. Let Ω be a group with identity e, W = ⊕g∈Ω Wg a Ω-graded commutative ring, C = ⊕g∈Ω Cg a graded W-module, and P = ⊕g∈Ω Pg a graded ideal of W. A proper graded submodule U of C is identified as a graded Pe-Jgr-primary submodule if, whenever rg ch ∈ U\Pe U for rg ∈ h(W) and ch ∈ h(C), then either ch ∈ U + Jgr (C) or rg ∈ Gr((U + Jgr (C) :W C)), where Jgr (C) denotes the graded Jacobson radical of C. The paper presents some results concerning the properties and behaviors of this class of graded submodules.

Keywords

gr-Pe-Jgr-primary submodules gr-Jgr-primary submodules gr-primary submodules

Subject Classifications

13A0216W50

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