Prime generalized alternative rings with nontrivial idempotent
Abstract: A generalized alternative ring is a nonassociative ring in which the identities ; and are identically zero. It is demonstrated here that if is a ring of this type with characteristic different from two and three, then semiprime with idempotent implies that has a Peirce decomposition relative to . Furthermore, if is prime and ; then must be alternative.
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Keywords: Generalized alternative ring , semiprime ring, Peirce decomposition, prime ring, alternative ring
Article copyright: © Copyright 1973 American Mathematical Society