The prime radical in alternative rings

Rich, Michael

doi:10.1090/S0002-9939-1976-0419547-3

The prime radical in alternative rings
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by Michael Rich

Proc. Amer. Math. Soc. 56 (1976), 11-15

DOI: https://doi.org/10.1090/S0002-9939-1976-0419547-3

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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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