SOME REMARKS ON GENERALIZATIONS OF MULTIPLICATIVELY CLOSED SUBSETS

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.