Abstract:
Let $\Phi$ be a unital associative commutative ring with $\frac12$. The local nilpotency is proved of binary Lie $\Phi$-algebras satisfying the third Engel condition. Moreover, it is proved that this class of algebras does not contain semiprime algebras.
Keywords:binary Lie algebra, Engel algebra, locally nilpotent algebra, semiprime algebra.