{"version":"1.0","published":"2016-09-05 01:57:54","provider_name":"Hatena Blog","author_url":"https://blog.hatena.ne.jp/derwind/","url":"https://randommemory.hatenablog.com/entry/2016/09/05/015754","provider_url":"https://hatena.blog","author_name":"derwind","html":"<iframe src=\"https://hatenablog-parts.com/embed?url=https%3A%2F%2Frandommemory.hatenablog.com%2Fentry%2F2016%2F09%2F05%2F015754\" title=\"\u98fd\u304d\u305f\u3089\u3084\u3081\u3088\u3046Galois\u7406\u8ad6(28)\u2015\u5177\u4f53\u4f8b - \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>","blog_url":"https://randommemory.hatenablog.com/","image_url":null,"width":"100%","categories":["math-alg"],"blog_title":"\u3089\u3093\u3060\u3080\u306a\u8a18\u61b6","title":"\u98fd\u304d\u305f\u3089\u3084\u3081\u3088\u3046Galois\u7406\u8ad6(28)\u2015\u5177\u4f53\u4f8b","type":"rich","height":"190","description":"\u8272\u3093\u306a\u4f8b\u306e\u7d9a\u304d\u3002\u82e6\u624b\u3060\u308e...\u3002$X^2+1 \\in \\R[X]$ \u306f\u65e2\u7d04\u306a\u306e\u3067\u3001 $\\R[X]/(X^2+1)$ \u306f\u4f53\u306b\u306a\u308b\u3002(\u98fd\u304d\u305f\u3089\u3084\u3081\u3088\u3046Galois\u7406\u8ad6(1)\u2015\u4f53\u3068\u65e2\u7d04\u591a\u9805\u5f0f - \u3089\u3093\u3060\u3080\u306a\u8a18\u61b6) \u5177\u4f53\u7684\u306b\u306f\u3001 $\\R[X]/(X^2+1) = \\{a + bX;\\ a,b \\in \\R\\} \\simeq \\C$ \u6216\u306f\u3001stem field\u3092\u601d\u3044\u51fa\u3057\u3066\u3001 $\\R[X]/(X^2+1) \\simeq \\R[\\sqrt{-1}] \\simeq \\C$ \u3068\u66f8\u3044\u305f\u307b\u3046\u304c\u3059\u3063\u304d\u308a\u3059\u308b\u304b\u3082\u3002\u3053\u308c\u3092\u4f7f\u3046\u3068\u3001 $\\C \\otimes_\\R \\C \\simeq \\C \\otimes_\\R \\R[X]/\u2026"}