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 → V | f ( α v ) = α f ( v ) C(R) = \{ f:V \to V|f(\alpha v) = \alpha f(v) for all α ∈ R , v ∈ V } \alpha \in R,v \in V\} the near-ring centralizer of R. We investigate the structure of C ( R ) C(R) and obtain a characterization of those rings R for which C ( R ) C(R) is a simple nonring.