{"type":"rich","width":"100%","url":"https://randommemory.hatenablog.com/entry/2016/09/05/023830","published":"2016-09-05 02:38:30","version":"1.0","provider_name":"Hatena Blog","title":"\u98fd\u304d\u305f\u3089\u3084\u3081\u3088\u3046Galois\u7406\u8ad6(29)\u2015\u5177\u4f53\u4f8b","categories":["math-alg"],"author_url":"https://blog.hatena.ne.jp/derwind/","blog_title":"\u3089\u3093\u3060\u3080\u306a\u8a18\u61b6","blog_url":"https://randommemory.hatenablog.com/","html":"<iframe src=\"https://hatenablog-parts.com/embed?url=https%3A%2F%2Frandommemory.hatenablog.com%2Fentry%2F2016%2F09%2F05%2F023830\" title=\"\u98fd\u304d\u305f\u3089\u3084\u3081\u3088\u3046Galois\u7406\u8ad6(29)\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>","author_name":"derwind","height":"190","description":"\u7d9a\u304d\u3002 $\\Q$-\u4ee3\u6570\u3068\u3057\u3066\u306e\u540c\u578b, $\\Q(\\sqrt{2})$-\u4ee3\u6570\u3068\u3057\u3066\u306e\u540c\u578b\u3068\u3057\u3066\u306e\u9023\u9396\u3067\u4ee5\u4e0b\u3092\u5f97\u308b\u3002$\\Q(\\sqrt{2}) \\otimes_\\Q \\Q(\\sqrt{3}) \\simeq \\Q(\\sqrt{2}) \\otimes_\\Q \\Q[X]/(X^2-3) \\simeq \\Q(\\sqrt{2})[X]/(X^2-3)$\u3053\u3053\u3067\u3001 $X^2-3$ \u306f $\\Q(\\sqrt{2})[X]$ \u3067\u3082\u65e2\u7d04\u306a\u306e\u3067\u3001$K = \\Q(\\sqrt{2})$ \u3068\u7f6e\u304f\u3068\u3001stem field \u3092\u8003\u3048\u308b\u3053\u3068\u3067\u3001\u4f53\u306e\u540c\u578b\u3068\u3057\u3066 $K[X]/(X^2 - 3) \\simeq K[\\sqrt{3}] = \\Q\u2026","image_url":null,"provider_url":"https://hatena.blog"}