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

Abstract

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 whenever \(abm \in N\) for some \(a, b \in R\) and \(m \in M\), then \(am \in N\) or \(bm \in N\) or \(ab \in (N :_R M)\). 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.