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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On free subalgebras of certain division algebras
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by Martin Lorenz PDF
Proc. Amer. Math. Soc. 98 (1986), 401-405 Request permission

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
  • L. Makar-Limanov, The skew field of fractions of the Weyl algebra contains a free noncommutative subalgebra, Comm. Algebra 11 (1983), no. 17, 2003–2006. MR 709019, DOI 10.1080/00927878308822945
    • —, On group rings of nilpotent groups, preprint.
  • Martin Lorenz, Group rings and division rings, Methods in ring theory (Antwerp, 1983) NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., vol. 129, Reidel, Dordrecht, 1984, pp. 265–280. MR 770597
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • 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