## Centralizer near-rings that are endomorphism rings

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- by Carlton J. Maxson and Kirby C. Smith
- Proc. Amer. Math. Soc.
**80**(1980), 189-195 - DOI: https://doi.org/10.1090/S0002-9939-1980-0577742-8
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## 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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## Bibliographic Information

- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**80**(1980), 189-195 - MSC: Primary 16A76; Secondary 16A44
- DOI: https://doi.org/10.1090/S0002-9939-1980-0577742-8
- MathSciNet review: 577742