{"height":"190","published":"2016-08-19 01:02:10","html":"<iframe src=\"https://hatenablog-parts.com/embed?url=https%3A%2F%2Frandommemory.hatenablog.com%2Fentry%2F2016%2F08%2F19%2F010210\" title=\"\u98fd\u304d\u305f\u3089\u3084\u3081\u3088\u3046Galois\u7406\u8ad6(8)\u2015stem field\u306e\u4e00\u610f\u6027 - \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","version":"1.0","width":"100%","provider_url":"https://hatena.blog","blog_title":"\u3089\u3093\u3060\u3080\u306a\u8a18\u61b6","url":"https://randommemory.hatenablog.com/entry/2016/08/19/010210","type":"rich","author_url":"https://blog.hatena.ne.jp/derwind/","blog_url":"https://randommemory.hatenablog.com/","description":"stem fields\u9593\u306e\u6e96\u540c\u578b\u5199\u50cf\u306b\u3064\u3044\u3066\u8003\u3048\u308b\u3002 \u4f53 $K$ \u4e0a\u306e $d$ \u6b21\u306e\u65e2\u7d04\u591a\u9805\u5f0f $P$ \u304c\u6839 $\\alpha,\\beta$ \u3092\u6301\u3064\u3068\u3057\u3066\u3001 $\\beta \\not\\in K[\\alpha]$ \u3068\u4eee\u5b9a\u3059\u308b\u3002 $K$-\u6e96\u540c\u578b\u5199\u50cf $\\varphi:K[\\alpha] \\to K[\\beta]$ \u3068\u3057\u3066\u306f\u3069\u3046\u3044\u3046\u3082\u306e\u304c\u8003\u3048\u3089\u308c\u308b\u304b\uff1f\u307e\u305a\u3001 $0 \\neq \\varphi$ \u306f\u5358\u5c04\u3067\u3042\u308b\u3002 $\\varphi(x) = 0,\\ x \\in K[\\alpha]$ \u3068\u3059\u308b\u6642\u3001 $x \\neq 0$ \u3068\u3059\u308b\u3068\u3001 $\\exists!\\, x^{-1} \\in K[\\alpha]$ \u304c\u3068\u308c\u308b\u306e\u3067\u3001\u2026","author_name":"derwind","image_url":null,"title":"\u98fd\u304d\u305f\u3089\u3084\u3081\u3088\u3046Galois\u7406\u8ad6(8)\u2015stem field\u306e\u4e00\u610f\u6027","categories":["math-alg"]}