On Homomorphic Images of Special Jordan Algebras

A linear algebra is called a Jordan algebra if it satisfies the identities (1) ab = ba, (a 2 b) a = a 2 (ba). It is well known that a linear algebra S over a field of characteristic different from two is a Jordan algebra if there is an isomorphism a → a of the vector-space underlying S into the vector-space of some associative algebra A such that 1 , where the dot denotes the multiplication in A . Such an algebra S is called a special Jordan algebra.