Weakly 2-Prime Sub-Modules

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.