Commutator products in skew Laurent series division rings
Rings and Algebras
2025-01-16 v1
Abstract
In 1965, Baxter established that a simple ring is either a field or that every one of its elements can be expressed as a sum of products of commutator pairs. In a recent paper, Gardella and Thiel demonstrated that every element in a noncommutative division ring can be represented as the sum of just two products of two commutators. They further posed the question of whether every element in a noncommutative division ring can be represented as the product of two commutators. In this paper, we affirmatively answer this question for skew Laurent series division rings over fields.
Keywords
Cite
@article{arxiv.2501.08638,
title = {Commutator products in skew Laurent series division rings},
author = {Hau-Yuan Jang and Wen-Fong Ke},
journal= {arXiv preprint arXiv:2501.08638},
year = {2025}
}