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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Rings with idempotents in their nuclei


Author: Michael Rich
Journal: Trans. Amer. Math. Soc. 208 (1975), 81-90
MSC: Primary 17A99
DOI: https://doi.org/10.1090/S0002-9947-1975-0371972-9
MathSciNet review: 0371972
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Abstract: Let $ R$ be a prime nonassociative ring. If the set of idempotents of $ R$ is a subset of the nucleus of $ R$ or of the alternative nucleus of $ R$ then it is shown that $ R$ is respectively an associative or an alternative ring. Also if $ R$ has one idempotent $ \ne 0,1$ which is in the Jordan nucleus or in the noncommutative Jordan nucleus then it is shown that $ R$ is respectively a Jordan or a noncommutative Jordan ring.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0371972-9
Keywords: Alternative nucleus, Jordan nucleus, noncommutative Jordan nucleus, flexible, idempotent, prime ring
Article copyright: © Copyright 1975 American Mathematical Society