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On free subsemigroups of skew fields


Author: L. Makar-Limanov
Journal: Proc. Amer. Math. Soc. 91 (1984), 189-191
MSC: Primary 16A39; Secondary 16A25, 16A70, 20M05
DOI: https://doi.org/10.1090/S0002-9939-1984-0740167-X
MathSciNet review: 740167
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Abstract: I will prove in this note that the multiplicative group of a skew field with uncountable center either contains a free nonabelian subsemigroup or is commutative.


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

  • [1] A. Lichtman, Normal subgroups of the multiplicative group of a skew field, Soviet Math. Dokl. 153 (1963), 1425-1429.
  • [2] -, Free subgroups of normal subgroups of the multiplicative group of skew field, Proc. Amer. Math. Soc. 71 (1978), 174-178. MR 0480623 (58:779)
  • [3] L. Makar-Limanov, On free subgroups of skew fields, preprint.
  • [4] I. Kaplansky, A theorem on division rings, Canad. J. Math. 3 (1951), 290-292. MR 0042389 (13:101g)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0740167-X
Article copyright: © Copyright 1984 American Mathematical Society

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