Strong Primeness of Hermitian Jordan Systems Original Research Article

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, * ) subset of or equal to J subset of or equal to H(Q(R), * ). This completes the converse of Zelmanovʹs classification of strongly prime Jordan systems, providing “if” as well as “only if” classifications of strongly prime and primitive Jordan systems.