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Vector space generated by the multiplicative commutators of a division ring

Aghabali, M ; Sharif University of Technology | 2013

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  1. Type of Document: Article
  2. DOI: 10.1142/S0219498813500436
  3. Publisher: 2013
  4. Abstract:
  5. Let D be a division ring with center 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 this paper it is shown that if D is algebraic over F and Char(D) = 0, then D = T(D). We conjecture that it is true in general. Among other results it is shown that in characteristic zero if T(D) is algebraic over F, then D is algebraic over F
  6. Keywords:
  7. Division ring ; Multiplicative commutator ; Trace function
  8. Source: Journal of Algebra and its Applications ; Volume 12, Issue 8 , December , 2013 ; 02194988 (ISSN)
  9. URL: http://www.worldscientific.com/doi/abs/10.1142/S0219498813500436