{"categories":["math-alg"],"version":"1.0","html":"<iframe src=\"https://hatenablog-parts.com/embed?url=https%3A%2F%2Frandommemory.hatenablog.com%2Fentry%2F2016%2F10%2F09%2F152846\" title=\"Galois\u7406\u8ad6(60)\u2015Kummer\u62e1\u5927(2) - \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>","width":"100%","type":"rich","author_url":"https://blog.hatena.ne.jp/derwind/","url":"https://randommemory.hatenablog.com/entry/2016/10/09/152846","height":"190","provider_url":"https://hatena.blog","published":"2016-10-09 15:28:46","image_url":null,"blog_url":"https://randommemory.hatenablog.com/","blog_title":"\u3089\u3093\u3060\u3080\u306a\u8a18\u61b6","description":"Galois\u7406\u8ad6(59)\u2015Kummer\u62e1\u5927(1) - \u3089\u3093\u3060\u3080\u306a\u8a18\u61b6\u306e\u9006\u3092\u8ff0\u3079\u308b\u3002 Prop \u4efb\u610f\u306e\u4f4d\u6570 $n$ \u306e\u5de1\u56de\u62e1\u5927 $L/K$ \u304c $(\\mathrm{char}(K),n) = 1$ \u3092\u6e80\u305f\u3059\u6642\u3001\u3042\u308b $a \\in K$ \u306b\u5bfe\u3057\u3066 $L = K(\\sqrt[n]{a})$ \u3068\u306a\u308b\u3002 proof $\\mathrm{Gal}(L/K) = \\langle \\sigma \\rangle$ \u3068\u3059\u308b\u3002\u4eee\u5b9a\u3088\u308a $\\sigma^n = id$ \u3067\u3042\u308b\u3002 Galois\u7406\u8ad6(41)\u2015\u30ac\u30ed\u30a2\u62e1\u5927 - \u3089\u3093\u3060\u3080\u306a\u8a18\u61b6\u3088\u308a\u3001 $[L:K] = \\#( \\mathrm{Gal}(L/K) ) = n$ \u3067\u2026","title":"Galois\u7406\u8ad6(60)\u2015Kummer\u62e1\u5927(2)","author_name":"derwind","provider_name":"Hatena Blog"}