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 Apr 22 revised Separable and purely inseparable extensions over fields of characteristic $p$ added 99 characters in body; edited tags Apr 20 asked Separable and purely inseparable extensions over fields of characteristic $p$ Apr 20 comment Order of a map $\Bbb F_{p^n}\to \Bbb F_{p^n}$which maps $x$ to $x^{p} -x$ My question is answered at math.stackexchange.com/questions/1384817/…. Plz close this post as it duplicated. Apr 20 revised Order of a map $\Bbb F_{p^n}\to \Bbb F_{p^n}$which maps $x$ to $x^{p} -x$ added 4 characters in body Apr 19 asked Order of a map $\Bbb F_{p^n}\to \Bbb F_{p^n}$which maps $x$ to $x^{p} -x$ Apr 14 comment char$(K)=0$ then $K(x^{2}) \cap K(x^{2}-x)=K$ Yes, you can close this if necessary. Actually I was searching for answers on our site but I couldn't find any. Jyrki's suggestion is really helpful. Apr 14 asked char$(K)=0$ then $K(x^{2}) \cap K(x^{2}-x)=K$ Apr 13 comment Definitions of length function on a Weyl group Thanks for the answer. That is helpful. Apr 13 accepted Definitions of length function on a Weyl group Apr 13 comment If $K \subset \mathbb{Q}(\sqrt[p]{2},\sqrt[q]{2})$ and $[K : \mathbb{Q}]=p$ then $K= \mathbb{Q}(\sqrt[p]{2})$ Great answer! You did use the assumption that \$p