M. Saheli - Department of Mathematics, Vali-e-Asr University of Rafsanjan,Rafsanjan, Iran.

Let R be a commutative ring, M be a unitary R-module and S(M) be the set of all submodules of M. Assume that ϕ : S(M) ! S(M) [ f∅g be a function. We say that aproper submodule N of M is ϕ-n-absorbing primary if a1; :::; an 2 R and x 2 M with a1:::anx 2 N n ϕ(N) implies a1:::an 2 (N : M) or the product of x with n

n-absorbing submodules, n-absorbing primary submodules, ϕ-n-absorbing primary submodules