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 $$a_1 a_2\ldots a_{n+1} m\in N$$ a 1 a 2 … a n + 1 m ∈ N for $$a_1, a_2,\ldots , a_{n+1}\in R$$ a 1 , a 2 , … , a n + 1 ∈ R and $$m \in M$$ m ∈ M , there are n of $$a_i$$ 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.