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Proceedings of the American Mathematical Society

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

 

 

Fully idempotent rings have regular centroids


Author: R. C. Courter
Journal: Proc. Amer. Math. Soc. 43 (1974), 293-296
MSC: Primary 16A32
DOI: https://doi.org/10.1090/S0002-9939-1974-0330217-0
MathSciNet review: 0330217
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Abstract: We prove that the centroid of a ring all of whose ideals are idempotent is commutative and regular in the sense of von Neumann. The center of a fully idempotent ring is regular. Evidently every regular ring is fully idempotent. One nonregular example is Sasiada's simple radical ring. A subring of the countably infinite row-finite matrices over Sasiada's ring provides an example of a nonsimple, indecomposable, nonregular fully idempotent ring.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0330217-0
Keywords: Von Neumann regular rings, duo rings, prime rings, semiprime rings, locally matrix rings
Article copyright: © Copyright 1974 American Mathematical Society