ON ALMOST 2-ABSORBING SUBMODULES

Abstract

Let R be a commutative ring with identity and let M be a unitary R-module.  A proper submodule N of an R-module M will be called almost 2-absorbing submodule if a, b ∈ R and m ∈ M with abm ∈ N — (N : M)N implies that ab ∈ (N : M) or am ∈ N, or bm ∈ N.  Also a proper ideal I of R will be called almost 2-absorbing ideal if a, b, c ∈ R with abc ∈ I — I² implies that ab ∈ I or ac ∈ I, or bc ∈ I.  These concepts are generalizations of the notions of 2-absorbing submodules and ideals respectively, which have been studied.  In this paper we give several results concerning almost 2-absorbing submodules.