Weakly approximately-prime submodules and related concepts

Abstract EN

Let R be a commutative ring with identity and P a unital left R-module .

The purpose of this paper is to introduce and study the concept of WAPP-prime submodules as a generalization of weakly prime submodules , where a proper submodule L of an R-module P is called a WAPP-prime , if whenever 0≠re ϵ L for rϵR , eϵP , implies that either e or r[:R P] .

Several examples , characterizations and basic properties of this concept are given .Moreover many characterizations of WAPP-prime submodules in class of multiplication modules are introduced