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The Prime Radical in Alternative Rings

Michael Rich
Proceedings of the American Mathematical Society
Vol. 56, No. 1 (Apr., 1976), pp. 11-15
DOI: 10.2307/2041563
Stable URL: http://www.jstor.org/stable/2041563
Page Count: 5
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The Prime Radical in Alternative Rings
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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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