A new class of dual notions: S-co-r-submodules and S-co-n-submodules based on multiplicatively closed subsets

Let R be a commutative ring, M be an R-module and S\subseteq R be a multiplicatively closed subset of R. The purpose of this paper is to introduce and investigate the concepts of S-co-r-submodules and S-co-n-submodules by using the notion of a multiplicatively closed subset of R. A non-zero submodule N of M with Rad(Ann(M))\cap S=\emptyset is called an S-co-n-submodule, if there exists s\in S such that whenever aN\subseteq K and sa\not \in Rad(Ann(M)) for some a\in R and a submodule K of M, then sN\subseteq K. Many properties and examples are given of such submodules. Also, we state the correspondence between S-co-r-submodules and S-co-n-submodules.

کلیدواژه ها:

S-co-r-submodule ، S-co-n-submodule ، S-comultiplication module ، S-multiplication module