The amenability and non-amenability of skew fields

Elek, Gábor

doi:10.1090/S0002-9939-05-08128-1

The amenability and non-amenability of skew fields
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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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