Endomorphisms and Distributive Elements in Near-Rings Determined by Rings and Modules

Abstract

For a unitary, faithful R-module V, the centralizer near-ring determined by R and V, denoted by MR(V), contains, as a sub-ring, the set of distributive elements of MR(V), denoted by Dist(MR(V)). The ring Dist(MR(V)) always contains the ring EndR(V). In this paper we discuss conditions which force EndR(V) = Dist(MR(V)) as well as conditions which force MR(V) = Dist(MR(V)).