Work

Another Proof of Levitzki’s Theorem for Prime Rings and Application to k-skew Commuting Property

Year: 2026

Type: article

Abstract: In this paper, we provide another proof of Levitzki’s theorem for prime rings with k!-torsion-free using the Vandermonde determinant, which states that a prime ring contains no nonzero nilpotent left or right ideal. As an application of this theorem, we prove that the k-skew commuting element in torsion-free prime *-rings with nonsymmetric element must be zero without using any deep structural results from ring theory.

Source: Axioms

DOI: 10.3390/axioms15070472

Author: Yazhou Zhang

Institution: Taiyuan Normal University

Language: English

Topic: Rings, Modules, and Algebras

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: National Natural Science Foundation of China