Generalized 2-absorbing and strongly generalized 2-absorbing second submodules

چکیده مقاله

Let R be a commutative ring with identity. A proper submodule N of an R-module M is said to be a 2-absorbing submodule of M if wheneverabm ∈ N for some a,b ∈ R and m ∈ M, then am ∈ N or bm ∈ N or ab ∈ (N:_R M). In [3], the authors introduced two dual notion of 2-absorbing submodules (that is, 2-absorbing and strongly 2-absorbing second submodules) of M and investigated some properties of these classes of modules. In this paper, we will introduce the concepts of generalized 2-absorbing and strongly generalized 2-absorbing second submodules of modules over a commutative ring and obtain some related results. © Algebra and Discrete Mathematics.