TY - JOUR
AU - M. Aaghabali
AU - Z. Tajfirouz
PY - 2020/05/06
Y2 - 2020/08/15
TI - Remarks on vector space generated by the multiplicative commutators of a division ring
JF - MATHEMATICA SCANDINAVICA
JA - MathScand
VL - 126
IS - 2
SE - Articles
DO - 10.7146/math.scand.a-116324
UR - https://www.mscand.dk/article/view/116324
AB - Let $D$ be a division ring with centre $F$. An element of the form $xyx^{-1}y^{-1}\in D$ 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.
ER -