On n-generalized commutators and Lie ideals of rings
Rings and Algebras
2021-06-28 v1
Abstract
Let R be an associative ring.In the paper we study n-generalized commutators of rings and prove that if R is a noncommutative prime ring and n > 2, then every nonzero n-generalized Lie ideal of R contains a nonzero ideal. Therefore, if R is a noncommutative simple ring, then R = [R, . . . ,R]n. This extends a classical result due to Herstein (Portugal. Math., 1954). Some generalizations and related questions on n-generalized commutators and their relationship with noncommutative polynomials are also discussed.
Keywords
Cite
@article{arxiv.2106.13487,
title = {On n-generalized commutators and Lie ideals of rings},
author = {Peter V. Danchev and Tsiu-Kwen Lee},
journal= {arXiv preprint arXiv:2106.13487},
year = {2021}
}
Comments
35 pages