Document Type : Original Manuscript

Author

Department of Mathematics, Faculty of Sciences, Vali-e-Asr University of Rafsanjan , P.O.Box 518, Rafsanjan, Iran

Abstract

Let R be a commutative ring with identity and M
be a unitary R-module. In this paper we generalize the concept
multiplicatively closed subset of R and we study some properties
of these genaralized subsets of M. Among the many results in this
paper, we generalize some well-known theorems about multiplicatively
closed subsets of R to these generalized subsets of M. Also
we show that some other well-known results about multiplicatively
closed subsets of R are not valid for these generalized subsets of
M.

Keywords