On one-sided Lie nilpotent ideals of associative rings

Abstract

We prove that a Lie nilpotent one-sided ideal of an associative ring \(R\) is contained in a Lie solvable two-sided ideal of \(R\). An estimation of  derived length of such   Lie solvable ideal is obtained depending on the class of Lie nilpotency of the Lie nilpotent one-sided ideal of \(R.\) One-sided Lie nilpotent ideals contained in ideals generated by commutators of the form \([\ldots [ [r_1, r_{2}], \ldots ],  r_{n-1}], r_{n}]\) are also studied.