{"type":"rich","provider_url":"https://hatena.blog","height":"190","blog_title":"\u3089\u3093\u3060\u3080\u306a\u8a18\u61b6","version":"1.0","blog_url":"https://randommemory.hatenablog.com/","width":"100%","html":"<iframe src=\"https://hatenablog-parts.com/embed?url=https%3A%2F%2Frandommemory.hatenablog.com%2Fentry%2F2016%2F09%2F19%2F141010\" title=\"Galois\u7406\u8ad6(42)\u2015\u30ac\u30ed\u30a2\u7fa4\u3068Artin\u306e\u5b9a\u7406 - \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>","provider_name":"Hatena Blog","author_name":"derwind","title":"Galois\u7406\u8ad6(42)\u2015\u30ac\u30ed\u30a2\u7fa4\u3068Artin\u306e\u5b9a\u7406","published":"2016-09-19 14:10:10","url":"https://randommemory.hatenablog.com/entry/2016/09/19/141010","image_url":null,"description":"Def $L/K$: \u30ac\u30ed\u30a2\u62e1\u5927\u3068\u3059\u308b\u3002 $G = \\mathrm{Gal}(L/K) := \\mathrm{Aut}(L/K)$ \u3092\u30ac\u30ed\u30a2\u7fa4\u3068\u547c\u3076${}_\\square$ Remark Galois\u7406\u8ad6(41)\u2015\u30ac\u30ed\u30a2\u62e1\u5927 - \u3089\u3093\u3060\u3080\u306a\u8a18\u61b6\u306e\u6700\u5f8c\u306e\u4e3b\u5f35\u3092\u66f8\u304d\u76f4\u3059\u3068 $L^{\\mathrm{Gal}(L/K)} = K$ \u3068\u306a\u308b\u3002 Theorem (Artin) $L$: \u4f53\u3002 $G \\subset \\mathrm{Aut}(L)$ (1) $G$ \u306e $L$ \u3078\u306e\u4f5c\u7528\u3067\u73fe\u308c\u308b $G$-\u8ecc\u9053\u304c\u6709\u9650\u8ecc\u9053(\u8ecc\u9053\u306e\u5143\u304c\u6709\u9650\u500b)\u3067\u3042\u308b\u6642\u3001 $L$ \u306f $L^G$ ($L$ \u306e $G$-\u4e0d\u5909\u4f53 or \u2026","author_url":"https://blog.hatena.ne.jp/derwind/","categories":["math-alg"]}