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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On rings satisfying $ [(a,\,b,\,c),\,d]=0$


Author: Armin Thedy
Journal: Proc. Amer. Math. Soc. 29 (1971), 250-254
MSC: Primary 17A30
MathSciNet review: 0294432
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Abstract: A simple nonassociative ring, in which the associators commute with all elements, is under mild additional assumptions either associative or commutative. This result cannot be extended to prime rings since a construction of semiprime rings gives counterexamples.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0294432-4
PII: S 0002-9939(1971)0294432-4
Keywords: Nonassociative ring, standard ring, standard algebra, $ (\gamma ,\delta )$-ring, semiprime ring, simple ring
Article copyright: © Copyright 1971 American Mathematical Society