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Proceedings of the American Mathematical Society

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

 
 

 

The prime radical in alternative rings


Author: Michael Rich
Journal: Proc. Amer. Math. Soc. 56 (1976), 11-15
MSC: Primary 17D05
DOI: https://doi.org/10.1090/S0002-9939-1976-0419547-3
MathSciNet review: 0419547
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Abstract: The characterization by J. Levitzki of the prime radical of an associative ring $R$ as the set of strongly nilpotent elements of $R$ is adapted here to apply to a wide class of nonassociative rings. As a consequence it is shown that the prime radical is a hereditary radical for the class of alternative rings and that the prime radical of an alternative ring coincides with the prime radical of its attached Jordan ring.


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Keywords: Alternative ring, <IMG WIDTH="15" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$s$">-ring, prime radical, hereditary radical
Article copyright: © Copyright 1976 American Mathematical Society