On one-sided Lie nilpotent ideals of associative rings

TL;DR

This paper proves that Lie nilpotent one-sided ideals in associative rings are contained within Lie solvable two-sided ideals and provides estimates for their derived length, advancing understanding of their structure.

Contribution

It introduces new results linking Lie nilpotent one-sided ideals to Lie solvable two-sided ideals and estimates their derived length based on nilpotency class.

Findings

Lie nilpotent one-sided ideals are contained in Lie solvable two-sided ideals

Derived length of such ideals depends on their Lie nilpotency class

Studied ideals generated by specific commutators

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.