Centralizer near-rings that are endomorphism rings

Maxson, Carlton J.; Smith, Kirby C.

doi:10.1090/S0002-9939-1980-0577742-8

Centralizer near-rings that are endomorphism rings
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by Carlton J. Maxson and Kirby C. Smith PDF

Proc. Amer. Math. Soc. 80 (1980), 189-195 Request permission

Abstract:

For a finite ring R with identity and a finite unital R-module V the set $C(R;V) = \{ f:V \to V|f(\alpha v) = \alpha f(v)$ for all $\alpha \in R,v \in V\}$ is the centralizer near-ring determined by R and V. Those rings R such that $C(R;V)$ is a ring for every R-module V are characterized. Conditions are given under which $C(R;V)$ is a semisimple ring. It is shown that if $C(R;V)$ is a semisimple ring then $C(R;V) = {\text {End}_R}(V)$.

References

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