{"type":"rich","categories":["math-alg"],"published":"2016-09-03 22:41:35","author_name":"derwind","blog_url":"https://randommemory.hatenablog.com/","url":"https://randommemory.hatenablog.com/entry/2016/09/03/224135","html":"<iframe src=\"https://hatenablog-parts.com/embed?url=https%3A%2F%2Frandommemory.hatenablog.com%2Fentry%2F2016%2F09%2F03%2F224135\" title=\"\u98fd\u304d\u305f\u3089\u3084\u3081\u3088\u3046Galois\u7406\u8ad6(26)\u2015\u6709\u9650K-\u4ee3\u6570\u306e\u69cb\u9020\u5b9a\u7406 - \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>","title":"\u98fd\u304d\u305f\u3089\u3084\u3081\u3088\u3046Galois\u7406\u8ad6(26)\u2015\u6709\u9650K-\u4ee3\u6570\u306e\u69cb\u9020\u5b9a\u7406","height":"190","description":"Theorem (\u6709\u9650 $K$-\u4ee3\u6570\u306e\u69cb\u9020\u5b9a\u7406) $K$: \u4f53, $A$: $K$-\u4ee3\u6570\u3002 $\\dim_K A (1)$A$ \u306e\u6975\u5927\u30a4\u30c7\u30a2\u30eb\u306f\u9ad8\u3005\u6709\u9650\u500b\u3067\u3042\u308b\u3002($m_1,\\cdots, m_r$) (2)$J := m_1 \\cap \\cdots \\cap m_r = \\prod m_j$ \u3068\u3059\u308b\u6642\u3001\u3042\u308b $n \\in \\N$ \u306b\u5bfe\u3057\u3066 $J^n = 0$ \u3067\u3042\u308b\u3002 (3)$A \\simeq A/m_1^{n_1} \\times \\cdots \\times A/m_r^{n_r} \\ \\text{for}\\ \\exists n_1,\\cdots,n_r$ \u4f8b $K[X]/(X^2\\cdot(\u2026","provider_name":"Hatena Blog","width":"100%","version":"1.0","image_url":null,"provider_url":"https://hatena.blog","author_url":"https://blog.hatena.ne.jp/derwind/","blog_title":"\u3089\u3093\u3060\u3080\u306a\u8a18\u61b6"}