Original language | English |
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Publisher | ArXiv |
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Number of pages | 3 |
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Publication status | Submitted - 3 Jul 2017 |
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Let D be a division ring with centre F. An element of the form xyx−1y−1∈ D 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.
ID: 43908122