Abstract
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.
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