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 a 1 a 2… an+ 1 m∈ N for a_1, a_2, ..., a_ n+ 1 ∈ R a 1, a 2,…,
an+ 1∈ R and m ∈ M m∈ M, there are n of a_i ai's whose product with m is in N …

In this paper, we introduce the notion of classical n-absorbing submodules of a module M
over a commutative ring R with identity, which is a generalization of classical prime
submodules. A proper submodule N of M is said to be classical n-absorbing if whenever a 1
a 2... a n+ 1 m in M, for a 1 a 2... a n+ 1 in R and m in M, then there are n of the ai's whose
product with m is in N. We give some basic results concerning classical n-absorbing
submodules. Then the classical n-absorbing avoidance theorem for submodules is proved …