Remarks on vector space generated by the multiplicative commutators of a division ring

• M. Aaghabali ^[1] ; Z. Tajfirouz ^[1]
  1. [1] University of Edimburgh (Reino Unido)
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 126, Nº 2, 2020, págs. 161-164
• Idioma: inglés
• DOI: 10.7146/math.scand.a-116324
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let D be a division ring with centre F. An element of the form xyx−1y−1∈D 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.