Eater ideals in Jordan algebras (Q1380043)

The so called \(n\)-tad eaters play a key role in the description of the strongly prime Jordan algebras by \textit{E. I. Zelmanov} [Sib. Math. J. 24, 73-85 (1993); translation from Sib. Mat. Zh. 24, 89-104 (1983; Zbl 0534.17009)]. The extension of this description to quadratic Jordan algebras requires more definitions of different ideals of \(n\)-tad eaters in the free special Jordan algebra. The aim of this paper is to study and clarify the relationships of these ideals. In particular, the ideal of hearty \(n\)-tad eaters is shown to coincide with that of imbedded \(n\)-tad eaters without any restriction on the ring of scalars.