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arXiv · 2106.13487

On n-generalized commutators and Lie ideals of rings

Peter V. Danchev·Tsiu-Kwen Lee
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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.

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Peter V. Danchev, Tsiu-Kwen Lee. 2021-06-25. On n-generalized commutators and Lie ideals of rings. https://arxiv.org/abs/2106.13487

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