TY - JOUR AU - Aaghabali, M. AU - Tajfirouz, Z. PY - 2020/05/06 Y2 - 2024/03/28 TI - Remarks on vector space generated by the multiplicative commutators of a division ring JF - MATHEMATICA SCANDINAVICA JA - Math. Scand. VL - 126 IS - 2 SE - Articles DO - 10.7146/math.scand.a-116324 UR - https://www.mscand.dk/article/view/116324 SP - 161-164 AB - <p>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.&nbsp;Aghabali et al., J. Algebra Appl. 12 (2013), no.&nbsp;8, art.&nbsp;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.</p> ER -