SOME REMARKS ON GENERALIZATIONS OF MULTIPLICATIVELY-CLOSED SUBSETS

Abstract. Let R be a commutative ring with an identity, and M be a unitary R-module. In this paper, the concept of multiplicatively- closed subset of R is generalized, and some properties of the generalized subsets of M are studied. Some well-known theorems about multiplicatively-closed subsets of R are also generalized, and it is shown that some other well-known results are not valid for M.