Commutator products in skew Laurent series division rings

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.