Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article

Generalized rational identities of subnormal subgroups of skew fields

Author(s): Katsuo Chiba
Journal: Proc. Amer. Math. Soc. 124 (1996), 1649-1653.
MSC (1991): Primary 16R50; Secondary 16K40
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: Let $D$ be a skew field with infinite center $K$ such that $[D:K]=\infty$ , and let $H$ be a non-central subnormal subgroup of the multiplicative group $D^*=D\backslash \{0\}$ of $D$ . Then there are no non-trivial generalized rational identities of $H$ . This generalizes a theorem proved by Makar-Limanov.

References:

1.: G. M. Bergman, The diamond lemma for ring theory, Adv. in Math. 29 (1978), 178--218. MR 81b:16001
2.: K. Chiba, Skew fields with a non-trivial generalized power central rational identity, Bull. Austral. Math. Soc. 49 (1994), 85--90. MR 95b:16017
3.: P. M. Cohn, Skew field constructions, London Math. Soc. Lecture Notes Ser., vol. 27, Cambridge Univ. Press, Cambridge and New York, 1977. MR 57:3190
4.: ------, Free rings and their relations, 2nd ed., Academic Press, New York, 1985. MR 87e:16006
5.: J. Z. Goncalves and A. Mandel, Are there free groups in division ring? Israel J. Math. 53 (1986), 69--80. MR 88a:16036
6.: L. Makar-Limanov, On subnormal subgroups of skew fields, J. Algebra 114 (1988), 261--267. MR 89d:16024


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS