Large Free Algebras in the Ring of Fractions of Skew Polynomial Rings |
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| Authors: | Shirvani M; Goncalves J Z |
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| Institution: | 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 |
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| Abstract: | It is shown that the division ring of quotients of a skew polynomialring of automorphism type, if infinite-dimensional over itscentre k and satisfying suitable hypotheses, contains the groupalgebra of a free group of large rank (usually at least |k|).The result applies, in particular, to the skew polynomial ringsconstructed from rational function fields, and affirmativelysettles the conjectures of Makar–Limanov and Lichtmanin this case. |
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