Primitive Jordan triple systems (Q1320696)

The classification of the nondegenerate prime Jordan triple systems (JTS) was obtained by \textit{E. Zelmanov} [Sib. Math. J. 26, 55-64 (1985; Zbl 0575.17012); translation from Sib. Mat. Zh. 26, No. 1, 71-82 (1985)]. The author of the paper under review deals with an analogous task for primitive JTS. The classification obtained reduces the primitive JTS to the simple ones and to JTS connected to primitive associative algebras. The methods used seem prospectful for further investigations. Among the most important ones it should be noted that a construction of a pentad-- eating ideal in the free special JTS is given. Compared to its analog known earlier it is simpler to handle and, moreover, it is generated by a polynomial of degree 19.