Simple near-ring centralizers of finite rings

Maxson, Carlton J.; Smith, Kirby C.

doi:10.1090/S0002-9939-1979-0529202-X

Simple near-ring centralizers of finite rings
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by Carlton J. Maxson and Kirby C. Smith PDF

Proc. Amer. Math. Soc. 75 (1979), 8-12 Request permission

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.

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