Primitivity in Jordan Systems is Ubiquitous,

The main result of the paper asserts that if a Jordan pairV = (V + , V − ) is (σ)-primitive at some 0 ≠ b V − σ, then it is ( ± )-primitive at any 0 ≠ b′ V . Also, if a Jordan triple systemTis primitive at some 0 ≠ b T, then it is primitive at any 0 ≠ b′ T. As a tool, similar results concerning one-sided primitivity and * -primitivity of associative pairs and triple systems are established. Equivalences between our definitions of primitivity and some other appearing in the literature are also obtained as a consequence.