Remarks on Vector Space Generated by the Multiplicative Commutators of a Division Ring
Rings and Algebras
2020-05-08 v2
Abstract
Let D be a division ring with centre F. Let T(D) be the vector space over F generated by all multiplicative commutators in D. In [1], 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.
Cite
@article{arxiv.1707.00658,
title = {Remarks on Vector Space Generated by the Multiplicative Commutators of a Division Ring},
author = {Mehdi Aaghabali and Zakeieh Tajfirouz},
journal= {arXiv preprint arXiv:1707.00658},
year = {2020}
}