{"url":"https://randommemory.hatenablog.com/entry/2016/09/03/185523","html":"<iframe src=\"https://hatenablog-parts.com/embed?url=https%3A%2F%2Frandommemory.hatenablog.com%2Fentry%2F2016%2F09%2F03%2F185523\" title=\"\u3069\u3063\u304b\u306b\u30e1\u30e2\u3063\u305f\u3063\u3051\uff1f - \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","categories":["math-alg"],"version":"1.0","description":"Lemma $R$: \u74b0\u3002 $M $: $R$-\u81ea\u7531\u52a0\u7fa4\u3068\u3057\u3001\u305d\u306e\u57fa\u5e95\u306e\u6fc3\u5ea6\u3092\u6709\u9650\u3068\u3059\u308b\u3002\u3053\u306e\u6642\u3001$\\varphi \\in \\mathrm{Hom}_R(M,M)$ \u306f\u5358\u5c04\u3067\u3042\u308c\u3070\u5168\u5c04\u3068\u306a\u308a\u3001\u5f93\u3063\u3066(\u81ea\u5df1)\u540c\u578b\u5199\u50cf\u306b\u306a\u308b\u3002 proof $\\{e_j\\}_{1 \\leq j \\leq n}$ \u3092 $M $ \u306e\u57fa\u5e95\u3068\u3059\u308b\u3002 $\\{ \\varphi(e_j) \\}_{1 \\leq j \\leq n}$ \u3082\u57fa\u5e95\u3067\u3042\u308b\u3053\u3068\u3092\u898b\u308b\u3002 $0 = \\sum_{j=1}^n a_j \\varphi(e_j) = \\varphi(\\sum_{j=1}^n a_j e_j)$ \u3068\u7f6e\u304f\u3068\u3001\u5358\u5c04\u6027\u3088\u308a $\\sum_{j\u2026","width":"100%","published":"2016-09-03 18:55:23","title":"\u3069\u3063\u304b\u306b\u30e1\u30e2\u3063\u305f\u3063\u3051\uff1f","height":"190","blog_url":"https://randommemory.hatenablog.com/","image_url":null,"author_url":"https://blog.hatena.ne.jp/derwind/","type":"rich","blog_title":"\u3089\u3093\u3060\u3080\u306a\u8a18\u61b6","provider_url":"https://hatena.blog","provider_name":"Hatena Blog"}