Simple Near-Ring Centralizers of Finite Rings

Abstract

For a finite ring R with identity and a finite unital R-module V we call $C(R) = \{ f:V \to V|f(\alpha v) = \alpha f(v)$ for all $\alpha \in R,v \in V\}$ the near-ring centralizer of R. We investigate the structure of $C(R)$ and obtain a characterization of those rings R for which $C(R)$ is a simple nonring.