{"height":"190","categories":["math-alg"],"author_url":"https://blog.hatena.ne.jp/derwind/","blog_title":"\u3089\u3093\u3060\u3080\u306a\u8a18\u61b6","title":"\u98fd\u304d\u305f\u3089\u3084\u3081\u3088\u3046Galois\u7406\u8ad6(19)\u2015\u5206\u96e2\u7684","image_url":null,"type":"rich","provider_name":"Hatena Blog","blog_url":"https://randommemory.hatenablog.com/","html":"<iframe src=\"https://hatenablog-parts.com/embed?url=https%3A%2F%2Frandommemory.hatenablog.com%2Fentry%2F2016%2F08%2F27%2F205731\" title=\"\u98fd\u304d\u305f\u3089\u3084\u3081\u3088\u3046Galois\u7406\u8ad6(19)\u2015\u5206\u96e2\u7684 - \u3089\u3093\u3060\u3080\u306a\u8a18\u61b6\" class=\"embed-card embed-blogcard\" scrolling=\"no\" frameborder=\"0\" style=\"display: block; width: 100%; height: 190px; max-width: 500px; margin: 10px 0px;\"></iframe>","url":"https://randommemory.hatenablog.com/entry/2016/08/27/205731","width":"100%","version":"1.0","author_name":"derwind","published":"2016-08-27 20:57:31","description":"\u5148\u306e\u547d\u984c\u306e $Q$ \u306b\u6ce8\u76ee\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u6027\u8cea\u304c\u3042\u3063\u305f\u3002 $Q$ \u304c\u65e2\u7d04\u3067 $(Q,Q^\\prime) = 1$ \u306a\u3089\u3070 $Q$ \u306f\u91cd\u6839\u3092\u6301\u305f\u306a\u3044\u3002\u3064\u307e\u308a\u3001 $Q$ \u306e\u6839\u306f\u3059\u3079\u3066\u7570\u306a\u308a\u3001splitting field \u306e\u4e2d\u3067 $\\mathrm{deg}(Q)$ \u500b\u306e\u5024\u3068\u3057\u3066\u5f97\u3089\u308c\u308b\u3002 Def $P \\in K[X]$ \u3092\u65e2\u7d04\u591a\u9805\u5f0f\u3068\u3059\u308b\u3002 $P$ \u304c\u5206\u96e2\u7684\u3067\u3042\u308b\u3068\u306f\u3001 $(P,P^\\prime) = 1$ \u306e\u6642\u3092\u8a00\u3046\u3002 $P(X) = Q(X^{p^r})$ \u3068\u3057\u3066(\u3053\u306e\u3088\u3046\u306a $r$ \u3068\u3057\u3066\u6700\u5927\u306e\u3082\u306e\u3092\u3068\u308b)\u3001 $d_{sep}(P) := \\mathrm{deg}(Q)$ \u3068\u304a\u304f\u3002($Q$ \u3092\u2026","provider_url":"https://hatena.blog"}