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 | References | Similar Articles | Additional Information
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.
- [1] A. Lichtman, Normal subgroups of the multiplicative group of a skew field, Soviet Math. Dokl. 153 (1963), 1425-1429.
- [2] A. I. Lichtman, Free subgroups of normal subgroups of the multiplicative group of skew fields, Proc. Amer. Math. Soc. 71 (1978), no. 2, 174–178. MR 480623, https://doi.org/10.1090/S0002-9939-1978-0480623-2
- [3] L. Makar-Limanov, On free subgroups of skew fields, preprint.
- [4] Irving Kaplansky, A theorem on division rings, Canad. J. Math. 3 (1951), 290–292. MR 42389, https://doi.org/10.4153/cjm-1951-033-7
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1984-0740167-X
Article copyright:
© Copyright 1984
American Mathematical Society
