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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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The amenability and non-amenability of skew fields
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by Gábor Elek PDF
Proc. Amer. Math. Soc. 134 (2006), 637-644 Request permission

Abstract:

We investigate the amenability of skew field extensions of the complex numbers. We prove that all skew fields of finite Gelfand-Kirillov transcendence degree are amenable. However there are both amenable and non-amenable finitely generated skew fields of infinite Gelfand-Kirillov transcendence degree.
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Additional Information
  • Gábor Elek
  • Affiliation: Mathematical Institute of the Hungarian Academy of Sciences, P.O. Box 127, H-1364 Budapest, Hungary
  • MR Author ID: 360750
  • Email: elek@renyi.hu
  • Received by editor(s): November 24, 2003
  • Received by editor(s) in revised form: June 15, 2004, and October 4, 2004
  • Published electronically: August 29, 2005
  • Communicated by: Martin Lorenz
  • © Copyright 2005 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 637-644
  • MSC (2000): Primary 12E15, 43A07
  • DOI: https://doi.org/10.1090/S0002-9939-05-08128-1
  • MathSciNet review: 2180879