Abstract
This paper establishes the strong primeness of all Jordan systemsJof hermitian type, trapped between ample hermitian elements of a ∗-prime associative systemRand its Martindale system of symmetric quotientsQ(R):H0(R,∗)⊆J⊆H(Q(R),∗). This completes the converse of Zelmanov's classification of strongly prime Jordan systems, providing “if” as well as “only if” classifications of strongly prime and primitive Jordan systems.
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