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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Kyung Hee Univ, Dept Math, Seoul 131701, South Korea
Kyung Hee Univ, Res Inst Basic Sci, Seoul 131701, South KoreaKyung Hee Univ, Dept Math, Seoul 131701, South Korea
Hong, Chan Yong
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Kim, Nam Kyun
Lee, Yang
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Pusan Natl Univ, Dept Math Educ, Pusan 609735, South KoreaKyung Hee Univ, Dept Math, Seoul 131701, South Korea