Remarks on vector space generated by the multiplicative commutators of a division ring - Aaghabali, M.; Tajfirouz, Z. (Mathematica Scandinavica, 2020)
Let D be a division ring with centre F. An element of the form xyx^-1y^-1D is called a multiplicative commutator. Let T(D) be the vector space over F generated by all multiplicative commutators in D. In M. Aghabali et al., J. Algebra Appl. 12 (2013), no. 8, art. 1350043, the authors have conjectured that every division ring is generated as a vector space over its centre by all of its multiplicative commutators. In this note it is shown that if D is centrally finite, then the conjecture holds.