{"html":"<iframe src=\"https://hatenablog-parts.com/embed?url=https%3A%2F%2Frandommemory.hatenablog.com%2Fentry%2F2016%2F08%2F28%2F001317\" title=\"\u98fd\u304d\u305f\u3089\u3084\u3081\u3088\u3046Galois\u7406\u8ad6(20)\u2015\u5206\u96e2\u6027\u306e\u540c\u5024\u6761\u4ef6 - \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","height":"190","published":"2016-08-28 00:13:17","version":"1.0","url":"https://randommemory.hatenablog.com/entry/2016/08/28/001317","blog_title":"\u3089\u3093\u3060\u3080\u306a\u8a18\u61b6","type":"rich","width":"100%","provider_url":"https://hatena.blog","blog_url":"https://randommemory.hatenablog.com/","author_url":"https://blog.hatena.ne.jp/derwind/","image_url":null,"author_name":"derwind","description":"$L/K$ \u3092\u6709\u9650\u6b21\u62e1\u5927\u3068\u3059\u308b\u3002 Def $[L:K]_{sep} := |\\mathrm{Hom}_K(L,\\bar{K})|$\u3082\u3057\u3001 $L=K(\\alpha)$ \u306e\u5834\u5408\u306b\u306f\u3001 $[L:K]_{sep}$ \u306f $\\alpha$ \u306e\u6700\u5c0f\u591a\u9805\u5f0f\u306e\u76f8\u7570\u306a\u308b\u6839\u306e\u500b\u6570\u3067\u3042\u308b\u3002($\\varphi \\in \\mathrm{Hom}_K(L,\\bar{K})$ \u306f $\\alpha$ \u3092\u5225\u306e\u6839\u306b\u3046\u3064\u3059\u306e\u3067\u3001\u305d\u306e\u5019\u88dc\u306e\u6570\u304c\u5206\u96e2\u6b21\u6570\u3068\u306a\u308b\u3002\u76f8\u7570\u306a\u308b\u6839\u306e\u6570 $\\leq \\deg(P_\\min(\\alpha, K)) = [L:K]$ \u3067\u3042\u308b\u306e\u3067\u3001 $[L:K]_{sep} \\leq [L:K]$ \u3067\u3042\u308b\u3002)$[L:\u2026","categories":["math-alg"],"title":"\u98fd\u304d\u305f\u3089\u3084\u3081\u3088\u3046Galois\u7406\u8ad6(20)\u2015\u5206\u96e2\u6027\u306e\u540c\u5024\u6761\u4ef6"}