The prime radical in alternative rings

Abstract

The characterization by J. Levitzki of the prime radical of an associative ring R R as the set of strongly nilpotent elements of R 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.