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On free subalgebras of certain division algebras


Author: Martin Lorenz
Journal: Proc. Amer. Math. Soc. 98 (1986), 401-405
MSC: Primary 16A39; Secondary 16A05, 16A06, 16A27
DOI: https://doi.org/10.1090/S0002-9939-1986-0857930-9
MathSciNet review: 857930
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Abstract: Using ideas of Makar-Limanov, we construct noncommutative free subalgebras in certain division algebras which arise as fields of fractions of skew polynomial rings. Our result applies in particular to the Weyl division algebra $ {D_1}$.


References [Enhancements On Off] (What's this?)

  • [ML1] L. Makar-Limanov, The skew field $ {D_1}$ contains free subalgebras, Comm. Algebra 11 (1983), 2003-2006. MR 709019 (84j:16012)
  • [ML2] -, On group rings of nilpotent groups, preprint.
  • [L] M. Lorenz, Group rings and division rings, Methods in Ring Theory (F. van Oystayen, ed.), Reidel, Dordrecht, 1984, pp. 265-280. MR 770597 (86d:16016)

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DOI: https://doi.org/10.1090/S0002-9939-1986-0857930-9
Article copyright: © Copyright 1986 American Mathematical Society

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