Nilpotent ideals in Lie and anti-Lie triple systems (Q1906632)

The author introduces a notion of nilpotent ideal for Lie and anti-Lie triple systems (of finite dimension over a field of characteristic \(\neq 2\)) which is different from the one given by \textit{N. Kamiya} [J. Algebra 158, 226-232 (1993)], and also notes that some of Kamiya's theorems are false. (See also the review of Kamiya's paper in Zbl 0790.17002.) She then proceeds to show the existence of a unique maximal nilpotent ideal in any (anti-) Lie triple system, which is called the nil radical. Over fields of characteristic 0 a generalization of Engel's theorem is shown to hold.