A characterization of nilpotent nonassociative algebras by invertible Leibniz-derivations

Moens proved that a finite-dimensional Lie algebra over a field of characteristic zero is nilpotent if and only if it has an invertible Leibniz-derivation. In this article we prove the analogous results for finite-dimensional Malcev, Jordan, (−1,1)(−1,1)-, right alternative, Zinbiel and Malcev-admissible noncommutative Jordan algebras over a field of characteristic zero. Also, we describe all Leibniz-derivations of semisimple Jordan, right alternative and Malcev algebras.