{"blog_title":"\u3089\u3093\u3060\u3080\u306a\u8a18\u61b6","image_url":null,"description":"$L/K$ \u3092\u30ac\u30ed\u30a2\u62e1\u5927\u3068\u3057 $[L:K] = n$ \u3068\u3059\u308b\u3002\u4eca\u5ea6\u306f $n = \\mathrm{char}(K)$ \u306e\u5834\u5408\u3092\u8003\u3048\u308b\u3002(Kummer \u62e1\u5927\u306e\u6642\u306b\u306f $(\\mathrm{char}(K),n)=1$ \u3092\u8003\u3048\u3066\u3044\u305f\u3002) \u3053\u306e\u30b1\u30fc\u30b9\u3067\u306e\u30ac\u30ed\u30a2\u62e1\u5927\u306f\u7279\u306bArtin-Schreier \u62e1\u5927\u3068\u547c\u3070\u308c\u308b\u3002 Theorem $p = \\mathrm{char}(K)$ \u3068\u3059\u308b\u3002 $P(X) = X^p - X - a \\in K[X]$ \u3068\u304a\u304f\u3002 \u3053\u306e\u6642\u3001 (1) $P$ \u306f\u65e2\u7d04\u3067\u3042\u308b\u304b(\u53ef\u7d04\u3067\u3042\u3063\u3066)\u5206\u89e3\u3059\u308b\u3002 (2a) $P$ \u304c\u65e2\u7d04\u306e\u6642\u3001 $\\alpha$ \u3092 $P$ \u306e\u6839\u3068\u3059\u308b\u3068 $K(\u2026","published":"2016-10-10 01:50:09","type":"rich","url":"https://randommemory.hatenablog.com/entry/2016/10/10/015009","author_name":"derwind","author_url":"https://blog.hatena.ne.jp/derwind/","version":"1.0","blog_url":"https://randommemory.hatenablog.com/","categories":["math-alg"],"html":"<iframe src=\"https://hatenablog-parts.com/embed?url=https%3A%2F%2Frandommemory.hatenablog.com%2Fentry%2F2016%2F10%2F10%2F015009\" title=\"Galois\u7406\u8ad6(61)\u2015Artin-Schreier \u62e1\u5927 - \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>","height":"190","provider_name":"Hatena Blog","title":"Galois\u7406\u8ad6(61)\u2015Artin-Schreier \u62e1\u5927","provider_url":"https://hatena.blog","width":"100%"}