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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The prime radical in alternative rings
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by Michael Rich PDF
Proc. Amer. Math. Soc. 56 (1976), 11-15 Request permission

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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Additional Information
  • © Copyright 1976 American Mathematical Society
  • 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