The Kostrikin radical and similar radicals of Lie algebras

The existing notion of the Kostrikin radical as a radical in the Kurosh–Amitsur sence on classes of Mal'tsev algebras over rings with $1/6$ is not completely justified. More precisely, to the full it is true for classes of Lie algebras over fields of characteristic zero and, as shown in the given paper, classes of algebraic Lie algebras of degree not greater than $n$ over rings with $1/n!$ at all ${n\geq 1}$. Similar conclusions are obtained in the paper also for the Jordan, regular, and extremal radicals constructed analogously to the Kostrikin radical.