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

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.