Weakly 2-Prime Sub-Modules

Mohammed Qader Rahman; Alaa A. Elewi; Mustafa Mohammed Hameed

doi:10.24996/ijs.2024.65.2.30

Authors

Mohammed Qader Rahman Republic of Iraq, Diyala Governorate, The General Directorate for Education of Diyala, https://orcid.org/0009-0004-7390-979X
Alaa A. Elewi Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
Mustafa Mohammed Hameed Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq,

DOI:

https://doi.org/10.24996/ijs.2024.65.2.30

Keywords:

prime sub-module, weakly prime sub-module, 2-prime sub-module, weakly 2-prime sub-module, proper sub-module

Abstract

Let R be a commutative ring containing a unit, and let be a left R-module. We define a proper sub-module N of an R-module M to be a weakly 2-prime sub-module if whenever , then either or . This concept is an expansion of the idea of a weakly 2-prime ideal, where an ideal P of R is said to be a weakly 2-prime ideal if for all implies or . Several characteristics of sub-modules that are weakly 2-prime are taken into account.