Rings of Homogeneous Functions Determined by Artinian Ring Modules Original Research Article

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