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Mar 22, 2018 at 10:56 comment added JOSE MANUEL GAMBOA MUTUBERRIA This is a very beautiful answer. Many thanks! I will try to find an automorphism of K(x) that does not maps K onto K, where K denotes the field you have found.
Mar 21, 2018 at 16:56 history answered Emil Jeřábek CC BY-SA 3.0