Piecewise Endomorphisms of Pid-Modules

Abstract

Let G be a finitely generated module over a PID, D. We investigate the structure of the centralizer near-ring MD(G) = {f: G → G ¦ f(ar) = (fa)r,a ∈ G, r ∈ D}. If C = {Gα} is a cover of G by maximal cyclic submodules then we show that every f ∈ MD(G) is piecewise an endomorphism of G.