On classicaln-absorbing submodules

Abstract

LetRa commutative ring with identity andMbe a unitaryR-module. In this paper, we investigate some properties ofn-absorbing submodules ofMas a generalization of 2-absorbing submodules. We also define the classicaln-absorbing submodule, a proper submoduleNof anR-moduleMis called a classicaln-absorbing submodule if whenevera1a2 horizontal ellipsis an+1m is an element of N\documentclass's whose product withmis inN. Furthermore, we give some characterizations ofn-absorbing and classicaln-absorbing submodules under some conditions.