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

Mehdi Aghabali, Z. Tajfirouz

Research output: Working paper

Abstract

Let D be a division ring with centre F. An element of the form xyx−1y−1D is called
a multiplicative commutator. 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.
Original languageEnglish
PublisherArXiv
Number of pages3
Publication statusSubmitted - 3 Jul 2017

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