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Journal of the London Mathematical Society 1999 60(2):481-489; doi:10.1112/S0024610799007772
© 1999 by London Mathematical Society
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© The London Mathematical Society

Large Free Algebras in the Ring of Fractions of Skew Polynomial Rings

M. Shirvani and J. Z. Gonçalves

Department of Mathematical Sciences, University of Alberta Edmonton, Alberta, Canada T6G 2G1 mazi{at}schur.math.ualberta.ca
Department of Mathematics, University of Sao Paulo Sao Paulo, Brazil jzg{at}ime.usp.br

Received 21 October 1996.

It is shown that the division ring of quotients of a skew polynomial ring of automorphism type, if infinite-dimensional over its centre k and satisfying suitable hypotheses, contains the group algebra of a free group of large rank (usually at least |k|). The result applies, in particular, to the skew polynomial rings constructed from rational function fields, and affirmatively settles the conjectures of Makar–Limanov and Lichtman in this case.


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