2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69291We 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.Rings and Algebras12E15; 43A07text