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 [...[[r1,r2],...],rn−1],rn] are also studied.Comment: 5 page