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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Centralizer near-rings that are endomorphism rings


Authors: Carlton J. Maxson and Kirby C. Smith
Journal: Proc. Amer. Math. Soc. 80 (1980), 189-195
MSC: Primary 16A76; Secondary 16A44
MathSciNet review: 577742
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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\vert 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)$.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0577742-8
Keywords: Centralizers, near-rings, semisimple rings
Article copyright: © Copyright 1980 American Mathematical Society