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Paper   IPM / M / 164
School of Mathematics
  Title:   On derived groups of division rings II
  Author(s): 
1.  S. Akbari-Feyzaabaadi
2.  M. Mahdavi-Hezavehi
3.  M. Mehraabaadi
4.  H. Hajiabolhassan
  Status:   Published
  Journal: Comm. Algebra
  No.:  8
  Vol.:  23
  Year:  1995
  Pages:   2881-2887
  Supported by:  IPM
  Abstract:
Let D be a division ring with centre F and denote by D′ the derived group (commutator subgroup) of D*=D−{0}. It is shown that if each element of D′ is algebraic over F, then D is algebraic over F. It is also proved that each finite separable extension of F in D is of the form F(c) for some element c in the derived group D′. Using these results, it is shown that if each element of the derived group D′ is of bounded degree over F, then D is finite dimensional over F.

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