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LARGE FREE ALGEBRAS IN THE RING OF FRACTIONS OF SKEW POLYNOMIAL RINGS

Published online by Cambridge University Press:  01 October 1999

M. SHIRVANI  and
J. Z. GONÇALVES
M. SHIRVANI
Affiliation:
Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1; mazi@schur.math.ualberta.ca
J. Z. GONÇALVES
Affiliation:
Department of Mathematics, University of Sao Paulo, Sao Paulo, Brazil; jzg@ime.usp.br
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Abstract

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 [mid ]k[mid ]). 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.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 60 , Issue 2 , October 1999 , pp. 481 - 489
Copyright
The London Mathematical Society 1999

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