J. Goncalves et M. Shirvani, ON FREE GROUP-ALGEBRAS IN DIVISION RINGS WITH UNCOUNTABLE CENTER, Proceedings of the American Mathematical Society, 124(3), 1996, pp. 685-687
Let D be a division algebra with uncountable center k. If D contains a
noncommutative free k-algebra, then D also contains the k-group algeb
ra of the free group of rank 2.