Abstract
In this paper, we extend Zel'manov's classification of linear Jordan systems (triple systems and pairs) of hermitian type to quadratic Jordan systems over an arbitrary ring of scalars. Using associative triple systems (of the first kind) for what we believe to be a more natural tool to describe special Jordan triples, we show that an i-special prime quadratic Jordan triple system (the ideals of which remain semiprime) with a nonzero hermitian part lies between an ample subspace of hermitian elements in a ∗-prime associative triple system and those in its Martindale system of symmetric quotients. Modulo some extra definitions, the structure of strongly prime Jordan pairs of hermitian type follows almost immediately from the Jordan triple result.
Published Version
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