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On one-sided Lie nilpotent ideals of associative rings. (English) Zbl 1164.16014
Summary: 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 the derived length of such a 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 \([\dots[[r_1,r_2],\dots],r_{n-1}],r_n]\) are also studied.
16W10 Rings with involution; Lie, Jordan and other nonassociative structures
16D25 Ideals in associative algebras