ON POLYNOMIAL IDENTITIES ON TRAIN ALGEBRAS OF RANK 3.

Alicia Labra, Cristian Reyes

Abstract


It is known that every train algebra of rank 2 is a Jordan algebra.
This is not true for train algebras of rank 3. In this paper we prove that
every train algebra of rank 3 satisfying a polynomial identity of degree
three is an associative algebra. We also prove that a train algebra of
rank 3 over fields of characteristic not 2,3,5 that satisfies a polynomial
identity of degree four is either a Jordan algebra or satisfies the identity
(xy)(xy)?(xx)(yy)=0. Moreover, in these algebras this last identity
does not oppose or imply the Jordan identity.

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