On Prime Right Alternative Algebras and Alternators

Abstract

<p>We study subvarieties of the variety of right alternative algebras over a field of characteristic t2,t3 such that the defining identities of the variety force the span of the alternators to be an ideal and do not force an algebra with identity element to be alternative. We call a member of such a variety a right alternative alternator ideal algebra. We characterize the algebras of this subvariety by finding an identity which holds if and only if an algebra belongs to the subvariety. We use this identity to prove that if R is a prime, right alternative alternator ideal algebra with an idempotent e to,tl such that (e,e,R) =O, then either R is alternative or R belongs to one of four exceptional varieties.</p>