{"width":"100%","version":"1.0","url":"https://randommemory.hatenablog.com/entry/2016/08/17/212439","provider_name":"Hatena Blog","html":"<iframe src=\"https://hatenablog-parts.com/embed?url=https%3A%2F%2Frandommemory.hatenablog.com%2Fentry%2F2016%2F08%2F17%2F212439\" title=\"\u98fd\u304d\u305f\u3089\u3084\u3081\u3088\u3046Galois\u7406\u8ad6(7)\u2015\u5206\u89e3\u4f53\u306e\u62e1\u5927\u6b21\u6570\u3092\u8003\u3048\u308b - \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_url":"https://hatena.blog","categories":["math-alg"],"height":"190","blog_url":"https://randommemory.hatenablog.com/","blog_title":"\u3089\u3093\u3060\u3080\u306a\u8a18\u61b6","author_url":"https://blog.hatena.ne.jp/derwind/","published":"2016-08-17 21:24:39","type":"rich","description":"\u300c\u4ee3\u6570\u6982\u8ad6\u300d\u7b2cV\u7ae0 \u4f8b2.11\u3088\u308a\u3002 $K = \\Q,\\ f(X) = X^3 - 5$ \u306b\u3064\u3044\u3066\u306e\u5206\u89e3\u4f53\u3002Eisenstein\u306e\u65e2\u7d04\u5224\u5b9a\u6cd5\u3092 $p=5$ \u306b\u5bfe\u3057\u3066\u4f7f\u3046\u3068 $f$ \u306f $\\Z[X]$ \u3067\u65e2\u7d04\u3001\u5f93\u3063\u3066Gauss\u306e\u88dc\u984c\u3088\u308a $\\Q[X]$ \u3067\u65e2\u7d04\u3067\u3042\u308b\u3053\u3068\u304c\u5206\u304b\u308b\u3002 \u6839\u306f $\\omega = \\frac{-1 + \\sqrt{-3}}{2}$ \u3068\u3057\u3066\u3001 $\\C$ \u306e\u7bc4\u56f2\u3067 $\\sqrt[3]{5},\\sqrt[3]{5}\\,\\omega,\\sqrt[3]{5}\\,\\omega^2$ \u3067\u3042\u308b\u3002\u307e\u305a\u3001$L = \\Q[\\sqrt[3]{5}]$ \u3068\u3059\u308b\u3068\u3001 $L[X]$ \u5185\u3067\u306f $(X \u2026","image_url":null,"author_name":"derwind","title":"\u98fd\u304d\u305f\u3089\u3084\u3081\u3088\u3046Galois\u7406\u8ad6(7)\u2015\u5206\u89e3\u4f53\u306e\u62e1\u5927\u6b21\u6570\u3092\u8003\u3048\u308b"}