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