Abstract:
We prove an analogue of the Bergen–Herstein–Lanski theorem for alternative
algebras: describe all alternative algebras that admit derivations with
invertible values. We also prove an analogue of Moens' theorem for alternative
algebras (a finite-dimensional alternative algebra over a field
of characteristic zero is nilpotent if and only if it admits an invertible
Leibniz derivation).
Keywords:derivation, alternative algebra, nilpotent algebra.