Some Aspects of Roughly Prime Submodules

Let R be a commutative ring with unity and M be an R-module. The aim of this article is to introduce and investigate certain properties of a new notion of prime submodules of a module, namely roughly prime submodules. A submodule N of M is said to be a roughly prime submodule of M if for rm ∈ N, r ∈ R and m ∈ M, implies that either m ∈ N + Z(M) or r ∈ (N + Z(M): M) where Z(M) is the singular submodule of M. The interaction of this submodule with other classes of modules as well as its characteristics in terms of direct sum, intersection and homomorphic image are studied along with the exploration of its behaviour in quotient modules.