Derivations and nil ideals (Q1123968)

It is shown that, in a torsion-free ring R, the Levitzki radical L, which is the largest locally nilpotent ideal of R, is invariant under all derivations d of R. The method is to show that the ideal \(L+d(L)\) is locally nilpotent, whence d(L)\(\subseteq L\). The corresponding result for the nilpotent radical was proved by the reviewer [J. Lond. Math. Soc., II. Ser. 10, 281-291 (1975; Zbl 0313.16011)].