초록
Let R be a commutative ring with 1, and let M be a (left) unitary R-module, let S = End(M) be the ring of R-endomorphisms of M. In this paper we look at some ring theoretic and module theoretic properties and try to see how do they transfer between R, S and M. Recall that an R-module M is said to be a multiplication R-module if each sub-module N of M has the form IM for some ideal I of R, [2]. In ${\S}1$ of this note we look at each of the Noetherian and Artinian properties and in ${\S}2$, we look at the regularity of R, and try to see how do they transfer to S.