## “School of Mathematics”

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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.