SOME REMARKS ON GENERALIZATIONS OF MULTIPLICATIVELY CLOSED SUBSETS

Abstract

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