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arXiv · 2501.08638

Commutator products in skew Laurent series division rings

Hau-Yuan Jang·Wen-Fong Ke
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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.

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Hau-Yuan Jang, Wen-Fong Ke. 2025-01-15. Commutator products in skew Laurent series division rings. https://arxiv.org/abs/2501.08638

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