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 $[...[[r_1,r_2],...],r_{n-1}],r_n]$ are also studied.

5 pages