ON SEMI-n-ABSORBING SUBMODULES

Let R be a commutative ring with identity and n a positive integer greater than 1. In this paper, we introduce the concept of semi-n-absorbing submodules. A proper submodule N of an R-module M is called a semi-n-absorbing submodule of M if whenever a \in R, x \in M and a^nx \in N then ax \in N ora^n \in (N :R M). A number of results concerning semi-n-absorbing submodulesand examples of them are given. It is shown that if N is a semi-n-absorbing submodule of M and F is a flat R-module such that F \otimes N is proper in F \otimes M then F \otimes N is semi-n-absorbing in F \otimes M. We show that the converse holds when F is faithfully flat.