The amenability and non-amenability of skew fields

Details The amenability and non-amenability of skew fields The amenability and non-amenability of skew fields

2003-11-21

arxiv.org/abs/math/0311375v1

Mathematics

Rings and Algebras

Scientific paper

We investigate the amenability of skew filed 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 skew
fields of infinite Gelfand-Kirillov transcendence degree. For example, the free
field is non-amenable.

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