{"categories":["math-alg"],"version":"1.0","url":"https://randommemory.hatenablog.com/entry/2016/09/20/004304","html":"<iframe src=\"https://hatenablog-parts.com/embed?url=https%3A%2F%2Frandommemory.hatenablog.com%2Fentry%2F2016%2F09%2F20%2F004304\" title=\"Galois\u7406\u8ad6(43)\u2015\u30ac\u30ed\u30a2\u62e1\u5927\u88dc\u8db3 - \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>","author_name":"derwind","blog_url":"https://randommemory.hatenablog.com/","height":"190","width":"100%","title":"Galois\u7406\u8ad6(43)\u2015\u30ac\u30ed\u30a2\u62e1\u5927\u88dc\u8db3","published":"2016-09-20 00:43:04","description":"Theorem $K$: \u4f53\u3068\u3059\u308b\u3002\u3053\u306e\u6642\u3001 $\\bar{K}/K$ \u304c\u30ac\u30ed\u30a2\u62e1\u5927 $\\iff$ $K$ \u306f\u5b8c\u5168\u4f53\u3002 proof ($\\Leftarrow$) \u98fd\u304d\u305f\u3089\u3084\u3081\u3088\u3046Galois\u7406\u8ad6(21)\u2015\u5b8c\u5168\u4f53 - \u3089\u3093\u3060\u3080\u306a\u8a18\u61b6\u3088\u308a\u3001$\\bar{K}$ \u306f $K$ \u4e0a\u5206\u96e2\u7684\u3067\u3042\u308b\u3002\u307e\u305f\u3001\u98fd\u304d\u305f\u3089\u3084\u3081\u3088\u3046Galois\u7406\u8ad6(40)\u2015\u6b63\u898f\u62e1\u5927 - \u3089\u3093\u3060\u3080\u306a\u8a18\u61b6\u3088\u308a\u3001 $\\bar{K}$ \u306f $K$ \u306e\u6b63\u898f\u62e1\u5927\u3067\u3042\u308b\u3002\u3088\u3063\u3066\u3001 $\\bar{K}/K$ \u306f\u30ac\u30ed\u30a2\u62e1\u5927\u3067\u3042\u308b\u3002 ($\\Rightarrow$) $K[X]$ \u306e\u65e2\u7d04\u591a\u9805\u5f0f\u306f\u305d\u306e\u6839 $\\in \\bar{K}$ \u306e\u6700\u5c0f\u591a\u9805\u5f0f\u3067\u3042\u308b\u304c\u3001\u4eee\u5b9a\u3088\u308a \u2026","provider_url":"https://hatena.blog","provider_name":"Hatena Blog","blog_title":"\u3089\u3093\u3060\u3080\u306a\u8a18\u61b6","author_url":"https://blog.hatena.ne.jp/derwind/","type":"rich","image_url":null}