Remarks on Vector Space Generated by the Multiplicative Commutators of a Division Ring

Published 3 Jul 2017 in math.RA | (1707.00658v2)

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.

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