Endomorphism Rings are Centralizer Near-rings

Abstract

For a finite ring R with identity and a finite unital R-module V the set C(R; V) = {f : V ->V : f(?v) = ?f(v) for all ? ? R, v ? V} is the centralizer near-ring determined by R and V. Rings R for witch C(R; V) is a ring for every R-module V, are characterized. Conditions are given under which C(R; V) is a semisimple centralizer near ring. Its shown that C(R; V) is a semisimple centralizer near ring then EndR(V) = C(R; V).GANIT J. Bangladesh Math. Soc.Vol. 34 (2014) 57-61