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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
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.
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- The London Mathematical Society 1999
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