On one-sided Lie nilpotent ideals of associative rings. (English) Zbl 1164.16014

Luchko, Victoriya S.; Petravchuk, Anatoliy P.

Algebra Discrete Math. 2007, No. 4, 102-107 (2007).

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.

MSC:

16W10	Rings with involution; Lie, Jordan and other nonassociative structures
16D25	Ideals in associative algebras

Keywords:

associative rings; one-sided ideals; Lie nilpotent ideals; derived lengths