On classical n-absorbing submodules

Let R a commutative ring with identity and M be a unitary R -module. In this paper, we investigate some properties of n -absorbing submodules of M as a generalization of 2-absorbing submodules. We also define the classical n -absorbing submodule, a proper submodule N of an R -module M is called a classical n -absorbing submodule if whenever a 1 a 2 … a n + 1 m ∈ N for a 1 , a 2 , … , a n + 1 ∈ R and m ∈ M , there are n of a i ’s whose product with m is in N . Furthermore, we give some characterizations of n -absorbing and classical n -absorbing submodules under some conditions.