In this paper we prove the existence and give precise descriptions of maximal algebras of Martindale like quotients for arbitrary strongly prime linear Jordan algebras. As a consequence, we show that Zelmanov's classification of strongly prime Jordan algebras can be viewed exactly as the description of their maximal algebras of Martindale-like quotients. As a side result, we show that the Martindale associative algebra of symmetric quotients can be expressed in terms of the symmetrized product, i.e., in purely Jordan terms.  2004 Elsevier Inc. All rights reserved.

In this paper we prove the inheritance of polynomial identities by covers of nondegenerate Jordan algebras satisfying certain ideal absorption properties. As a consequence we obtain the inheritance of speciality by Martindale-like covers, proving, in particular, that a Jordan algebra having a nondegenerate essential ideal which is special must be special.

In this paper we show that the scalar center of a nondegenerate quadratic Jordan algebra is contained in the scalar center of any of its Martindale-like covers.

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