On Weakly S-2-Absorbing Submodules

Abstract

Let R be a commutative ring with identity and let M be a unitary R-module. In this paper, we introduce the notion of weakly S-2-absorbing submodule. Suppose that S is a multiplicatively closed subset of R. A submodule P of M with (P:R M)∩S=∅ is said to be a weakly S-2-absorbing submodule if there exists an element s ∈ S such that whenever a,b∈R and m∈M with 0≠abm∈P, then sab∈(P: M) or sam∈P or sbm∈P. We give the characterizations, properties and examples of weakly S-2-absorbing submodules.