[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki\/archives\/7491#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki\/archives\/7491","headline":"\u5927\u57df\u4f53 – Wikipedia","name":"\u5927\u57df\u4f53 – Wikipedia","description":"\u6570\u5b66\u306b\u304a\u3044\u3066\u3001\u5927\u57df\u4f53\uff08\u305f\u3044\u3044\u304d\u305f\u3044\u3001\u82f1: global field\uff09\u3068\u306f\u3001\u6b21\u306e\u3044\u305a\u308c\u304b\u306e\u4f53\u306e\u3053\u3068\u3092\u8a00\u3046\u3002 \u4ed8\u5024\u8ad6\u3092\u901a\u3057\u305f\u3053\u308c\u3089\u306e\u4f53\u306e\u516c\u7406\u7684\u7279\u5fb4\u4ed8\u3051\u306f\u3001\u30a8\u30df\u30fc\u30eb\u30fb\u30a2\u30eb\u30c6\u30a3\u30f3 \u3068\u30b8\u30e7\u30fc\u30b8\u30fb\u30a6\u30a7\u30fc\u30d7\u30eb\uff08\u30d5\u30e9\u30f3\u30b9\u8a9e\u7248\uff09\u306b\u3088\u308a1940\u5e74\u4ee3\u306b\u4e0e\u3048\u3089\u308c\u305f[1]\u3002 \u3053\u306e2\u7a2e\u985e\u306e\u4f53\u306e\u9593\u306b\u306f\u5f62\u5f0f\u7684\u306a\u5171\u901a\u70b9\u304c\u3044\u304f\u3064\u304b\u3042\u308b\u3002\u3069\u3061\u3089\u306e\u4f53\u3082\u3001\u5b8c\u5099\u5316\u304c\u5e38\u306b\u5c40\u6240\u30b3\u30f3\u30d1\u30af\u30c8\u4f53\u3067\u3042\u308b\u3068\u3044\u3046\u6027\u8cea\u3092\u6301\u3063\u3066\u3044\u308b\uff08\u5c40\u6240\u4f53\u3092\u53c2\u7167\uff09\u3002\u3069\u3061\u3089\u306e\u4f53\u3082\u3001\u96f6\u3067\u306a\u3044\u5168\u3066\u306e\u30a4\u30c7\u30a2\u30eb\u304c\u6709\u9650\u6307\u6570\u3067\u3042\u308b\u30c7\u30c7\u30ad\u30f3\u30c8\u6574\u57df\u306e\u5206\u6570\u4f53\u3068\u3057\u3066\u5b9f\u73fe\u3067\u304d\u308b\u3002\u3069\u3061\u3089\u306e\u4f53\u3067\u3082\u3001\u96f6\u3067\u306a\u3044\u5143 x \u306e\u7a4d\u516c\u5f0f \u220fv|x|v=1{displaystyle prod _{v}|x|_{v}=1} \u304c\u6210\u308a\u7acb\u3064\u3002 2\u7a2e\u985e\u306e\u4f53\u306e\u9593\u306e\u985e\u4f3c\u306f\u3001\u4ee3\u6570\u7684\u6574\u6570\u8ad6\u306e\u5f37\u3044\u52d5\u6a5f\u4ed8\u3051\u3068\u306a\u3063\u3066\u304d\u305f\u3002\u6570\u4f53\u3068\u30ea\u30fc\u30de\u30f3\u9762\u306e\u985e\u4f3c\u3068\u3044\u3046\u8003\u3048\u65b9\u306f\u300119\u4e16\u7d00\u306e\u30ea\u30d2\u30e3\u30eb\u30c8\u30fb\u30c7\u30fc\u30c7\u30ad\u30f3\u30c8 (Richard Dedekind) \u3084\u30cf\u30a4\u30f3\u30ea\u30c3\u30d2\u30fb\u30a6\u30a7\u30fc\u30d0\u30fc\uff08\u82f1\u8a9e\u7248\uff09 (Heinrich M. Weber) \u307e\u3067\u9061\u308b\u3002\u4ee3\u6570\u66f2\u7dda\u3068\u3057\u3066\u306e\u30ea\u30fc\u30de\u30f3\u9762\u306e\u4e00\u5074\u9762\u304c\u6709\u9650\u4f53\u4e0a\u5b9a\u7fa9\u3055\u308c\u305f\u66f2\u7dda\u3078\u5199\u50cf\u3055\u308c\u308b\u3001’\u5927\u57df\u4f53’\u306e\u30a2\u30a4\u30c7\u30a2\u306b\u3088\u308b\u3088\u308a\u5f37\u3044\u985e\u4f3c\u306f\u30011930\u5e74\u4ee3\u306b\u4f5c\u308a\u4e0a\u3052\u3089\u308c\u30011940\u5e74\u306b\u30a2\u30f3\u30c9\u30ec\u30fb\u30f4\u30a7\u30a4\u30e6","datePublished":"2021-03-21","dateModified":"2021-03-21","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/cd810e53c1408c38cc766bc14e7ce26a?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/cd810e53c1408c38cc766bc14e7ce26a?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/d8a579a28bfd00315174fa08b6ae985395621eb9","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/d8a579a28bfd00315174fa08b6ae985395621eb9","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/jp\/wiki\/archives\/7491","about":["Wikipedia"],"wordCount":1132,"articleBody":"\u6570\u5b66\u306b\u304a\u3044\u3066\u3001\u5927\u57df\u4f53\uff08\u305f\u3044\u3044\u304d\u305f\u3044\u3001\u82f1: global field\uff09\u3068\u306f\u3001\u6b21\u306e\u3044\u305a\u308c\u304b\u306e\u4f53\u306e\u3053\u3068\u3092\u8a00\u3046\u3002  \u4ed8\u5024\u8ad6\u3092\u901a\u3057\u305f\u3053\u308c\u3089\u306e\u4f53\u306e\u516c\u7406\u7684\u7279\u5fb4\u4ed8\u3051\u306f\u3001\u30a8\u30df\u30fc\u30eb\u30fb\u30a2\u30eb\u30c6\u30a3\u30f3 \u3068\u30b8\u30e7\u30fc\u30b8\u30fb\u30a6\u30a7\u30fc\u30d7\u30eb\uff08\u30d5\u30e9\u30f3\u30b9\u8a9e\u7248\uff09\u306b\u3088\u308a1940\u5e74\u4ee3\u306b\u4e0e\u3048\u3089\u308c\u305f[1]\u3002\u3053\u306e2\u7a2e\u985e\u306e\u4f53\u306e\u9593\u306b\u306f\u5f62\u5f0f\u7684\u306a\u5171\u901a\u70b9\u304c\u3044\u304f\u3064\u304b\u3042\u308b\u3002\u3069\u3061\u3089\u306e\u4f53\u3082\u3001\u5b8c\u5099\u5316\u304c\u5e38\u306b\u5c40\u6240\u30b3\u30f3\u30d1\u30af\u30c8\u4f53\u3067\u3042\u308b\u3068\u3044\u3046\u6027\u8cea\u3092\u6301\u3063\u3066\u3044\u308b\uff08\u5c40\u6240\u4f53\u3092\u53c2\u7167\uff09\u3002\u3069\u3061\u3089\u306e\u4f53\u3082\u3001\u96f6\u3067\u306a\u3044\u5168\u3066\u306e\u30a4\u30c7\u30a2\u30eb\u304c\u6709\u9650\u6307\u6570\u3067\u3042\u308b\u30c7\u30c7\u30ad\u30f3\u30c8\u6574\u57df\u306e\u5206\u6570\u4f53\u3068\u3057\u3066\u5b9f\u73fe\u3067\u304d\u308b\u3002\u3069\u3061\u3089\u306e\u4f53\u3067\u3082\u3001\u96f6\u3067\u306a\u3044\u5143 x \u306e\u7a4d\u516c\u5f0f  \u220fv|x|v=1{displaystyle prod _{v}|x|_{v}=1}\u304c\u6210\u308a\u7acb\u3064\u30022\u7a2e\u985e\u306e\u4f53\u306e\u9593\u306e\u985e\u4f3c\u306f\u3001\u4ee3\u6570\u7684\u6574\u6570\u8ad6\u306e\u5f37\u3044\u52d5\u6a5f\u4ed8\u3051\u3068\u306a\u3063\u3066\u304d\u305f\u3002\u6570\u4f53\u3068\u30ea\u30fc\u30de\u30f3\u9762\u306e\u985e\u4f3c\u3068\u3044\u3046\u8003\u3048\u65b9\u306f\u300119\u4e16\u7d00\u306e\u30ea\u30d2\u30e3\u30eb\u30c8\u30fb\u30c7\u30fc\u30c7\u30ad\u30f3\u30c8 (Richard Dedekind) \u3084\u30cf\u30a4\u30f3\u30ea\u30c3\u30d2\u30fb\u30a6\u30a7\u30fc\u30d0\u30fc\uff08\u82f1\u8a9e\u7248\uff09 (Heinrich M. Weber) \u307e\u3067\u9061\u308b\u3002\u4ee3\u6570\u66f2\u7dda\u3068\u3057\u3066\u306e\u30ea\u30fc\u30de\u30f3\u9762\u306e\u4e00\u5074\u9762\u304c\u6709\u9650\u4f53\u4e0a\u5b9a\u7fa9\u3055\u308c\u305f\u66f2\u7dda\u3078\u5199\u50cf\u3055\u308c\u308b\u3001’\u5927\u57df\u4f53’\u306e\u30a2\u30a4\u30c7\u30a2\u306b\u3088\u308b\u3088\u308a\u5f37\u3044\u985e\u4f3c\u306f\u30011930\u5e74\u4ee3\u306b\u4f5c\u308a\u4e0a\u3052\u3089\u308c\u30011940\u5e74\u306b\u30a2\u30f3\u30c9\u30ec\u30fb\u30f4\u30a7\u30a4\u30e6 (Andr\u00e9 Weil) \u306b\u3088\u308a\u89e3\u6c7a\u3055\u308c\u305f\u6709\u9650\u4f53\u4e0a\u306e\u66f2\u7dda\u306e\u30ea\u30fc\u30de\u30f3\u4e88\u60f3\u3067\u5168\u76db\u3092\u304d\u308f\u3081\u305f\u3002\u7528\u8a9e\u306f\u30f4\u30a7\u30a4\u30e6\u306b\u3088\u308b\u306e\u3067\u3042\u308d\u3046\u3002\u5f7c\u306f Basic Number Theory (1967) \u3092\u51fa\u7248\u3057\u3001\u305d\u306e\u4e2d\u3067\u3053\u308c\u3089\u306e\u5e73\u884c\u6027\u3092\u8a18\u8ff0\u3057\u305f\u3002\u666e\u901a\u306f\u51fd\u6570\u4f53\u306e\u65b9\u304c\u5bb9\u6613\u3067\u5148\u306b\u9042\u884c\u3057\u3001\u6570\u4f53\u306e\u4e0a\u3067\u5e73\u884c\u3059\u308b\u30c6\u30af\u30cb\u30c3\u30af\u3092\u958b\u767a\u3059\u308b\u3002\u30a2\u30e9\u30b1\u30ed\u30d5\u7406\u8ad6\uff08\u82f1\u8a9e\u7248\uff09\u306e\u767a\u5c55\u3068\u30b2\u30eb\u30c8\u30fb\u30d5\u30a1\u30eb\u30c6\u30a3\u30f3\u30b0\u30b9 (Gerd Faltings) \u304c\u30e2\u30fc\u30c7\u30eb\u4e88\u60f3\u306e\u8a3c\u660e\u306b\u305d\u308c\u3092\u5229\u7528\u3057\u305f\u3053\u3068\u306f\u3001\u5287\u7684\u306a\u4f8b\u3067\u3042\u308b\u3002\u985e\u4f3c\u306f\u307e\u305f\u3001\u5ca9\u6fa4\u7406\u8ad6\u306e\u767a\u5c55\u3068\u5ca9\u6fa4\u4e3b\u4e88\u60f3\u3078\u3082\u5f71\u97ff\u3057\u3066\u3044\u308b\u3002\u30e9\u30f3\u30b0\u30e9\u30f3\u30ba\u30fb\u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u57fa\u672c\u88dc\u984c\uff08\u82f1\u8a9e\u7248\uff09\u306e\u8a3c\u660e\u3067\u3082\u3001\u6570\u4f53\u306e\u5834\u5408\u3092\u51fd\u6570\u4f53\u306e\u5834\u5408\u3078\u5e30\u7740\u3055\u305b\u308b\u30c6\u30af\u30cb\u30c3\u30af\u3092\u4f7f\u3063\u305f\u3002^ Artin & Whaples 1945 and Artin & Whaples 1946\u53c2\u8003\u6587\u732e[\u7de8\u96c6]Artin, Emil; Whaples, George (1945), \u201cAxiomatic characterization of fields by the product formula for valuations\u201d, Bull. Amer. Math. Soc. 51:  469\u2013492, doi:10.1090\/S0002-9904-1945-08383-9, MR0013145\u00a0Artin, Emil; Whaples, George (1946), \u201cA note on axiomatic characterization of fields\u201d, Bull. Amer. Math. Soc. 52:  245\u2013247, doi:10.1090\/S0002-9904-1946-08549-3, MR0015382\u00a0J.W.S. Cassels, “Global fields”, in J.W.S. Cassels and A. Frohlich (edd), Algebraic number theory, Academic Press, 1973.  Chap.II, pp.\u00a045\u201384.J.W.S. Cassels, “Local fields”, Cambridge University Press, 1986, ISBN 0-521-31525-5.  P.56.Neukirch, J\u00fcrgen; Schmidt, Alexander; Wingberg, Kay (2008), Cohomology of Number Fields, Grundlehren der Mathematischen Wissenschaften, 323 (Second ed.), Berlin: Springer-Verlag, ISBN\u00a0978-3-540-37888-4, Zbl\u00a01136.11001, MR2392026\u00a0\u5916\u90e8\u30ea\u30f3\u30af[\u7de8\u96c6]"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki\/archives\/7491#breadcrumbitem","name":"\u5927\u57df\u4f53 – Wikipedia"}}]}]