Rings of Homogeneous Functions Determined by Artinian Ring Modules

Abstract

Given an R-module V, the centralizer near-ring M R ( V) is the collection of all functions ƒ: V → V such that ƒ( vr) = ƒ( v) r, for all v ∈ V, r ∈ R with the operations of point-wise addition and composition of functions, In this paper necessary and/or sufficient conditions are found for M R ( V) to be a ring when R is a commutative local ring with nilpotent radical.