An elemental characterization of strong primeness in Jordan systems (Q1916399)

The authors give elemental characterizations of strong primeness for Jordan algebras, pairs and triple systems. Using \textit{K. McCrimmon}'s approach [Algebras Groups Geom. 1, 217-234 (1984; Zbl 0562.17006)] they prove that a Jordan pair \(V= (V^+, V^-)\) is strongly prime if and only if for all \(\sigma= \pm\) and \(a,b\in V^\sigma\), \(Q_a Q_b (V^\sigma) Q_b= 0\) implies \(a=0\) or \(b=0\). For a Jordan triple system an analogous condition for strong primeness is given. They use their characterization to study the transfer of strong primeness between a Jordan system and its local algebras and subquotients.