@prefix rdf: . @prefix dbr: . @prefix yago: . dbr:Algebraic_variety rdf:type yago:Collection107951464 , yago:WikicatPolynomials , yago:WikicatAlgebraicVarieties . @prefix dbo: . dbr:Algebraic_variety rdf:type dbo:Planet , yago:Relation100031921 , yago:Group100031264 , yago:Assortment108398773 , yago:Abstraction100002137 , yago:MathematicalRelation113783581 , yago:Function113783816 , yago:Polynomial105861855 . @prefix owl: . dbr:Algebraic_variety rdf:type owl:Thing . @prefix rdfs: . dbr:Algebraic_variety rdfs:label "Variedade alg\u00E9brica"@pt , "Rozmaito\u015B\u0107 algebraiczna"@pl , "Varietas aljabar"@in , "Algebra\u00EFsche vari\u00EBteit"@nl , "\uB300\uC218\uB2E4\uC591\uCCB4"@ko , "Algebraisk varietet"@sv , "\u4EE3\u6570\u7C07"@zh , "\u062A\u0646\u0648\u0639 \u062C\u0628\u0631\u064A"@ar , "Algebraische Variet\u00E4t"@de , "Algebra varia\u0135o"@eo , "Algebraic variety"@en , "Varietat algebraica"@ca , "\u0410\u043B\u0433\u0435\u0431\u0440\u0438\u0447\u043D\u0438\u0439 \u043C\u043D\u043E\u0433\u043E\u0432\u0438\u0434"@uk , "Variet\u00E0 algebrica"@it , "\u0391\u03BB\u03B3\u03B5\u03B2\u03C1\u03B9\u03BA\u03AE \u03C0\u03BF\u03B9\u03BA\u03B9\u03BB\u03AF\u03B1"@el , "Variedad algebraica"@es , "Algebraick\u00E1 varieta"@cs , "\u4EE3\u6570\u591A\u69D8\u4F53"@ja , "\u0410\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u043E\u0435 \u043C\u043D\u043E\u0433\u043E\u043E\u0431\u0440\u0430\u0437\u0438\u0435"@ru , "Vari\u00E9t\u00E9 alg\u00E9brique"@fr ; rdfs:comment "( \uC774 \uBB38\uC11C\uB294 \uB300\uC218\uAE30\uD558\uD559\uC5D0\uC11C \uBC29\uC815\uC2DD\uC758 \uD574\uC758 \uC9D1\uD569\uC5D0 \uAD00\uD55C \uAC83\uC785\uB2C8\uB2E4. \uC77C\uB828\uC758 \uD56D\uB4F1\uC2DD\uB4E4\uC744 \uB9CC\uC871\uC2DC\uD0A4\uB294 \uB300\uC218 \uAD6C\uC870\uB4E4\uC758 \uBAA8\uC784\uC5D0 \uB300\uD574\uC11C\uB294 \uB300\uC218 \uAD6C\uC870 \uB2E4\uC591\uCCB4 \uBB38\uC11C\uB97C \uCC38\uACE0\uD558\uC2ED\uC2DC\uC624.) \uB300\uC218\uAE30\uD558\uD559\uC5D0\uC11C \uB300\uC218\uB2E4\uC591\uCCB4(\u4EE3\u6578\u591A\u6A23\u9AD4, \uC601\uC5B4: algebraic variety)\uB294 \uAD6D\uC18C\uC801\uC73C\uB85C \uB2E4\uD56D\uC2DD\uB4E4\uB85C \uC8FC\uC5B4\uC9C0\uB294 \uBC29\uC815\uC2DD\uB4E4\uC758 \uC601\uC810 \uC9D1\uD569\uCC98\uB7FC \uBCF4\uC774\uB294 \uACF5\uAC04\uC774\uB2E4. \uACE0\uC804\uC801 \uB300\uC218\uAE30\uD558\uD559\uC5D0\uC11C \uB2E4\uB8E8\uB294 \uAE30\uBCF8\uC801\uC778 \uB300\uC0C1\uC774\uB2E4."@ko , "\u0410\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u043E\u0435 \u043C\u043D\u043E\u0433\u043E\u043E\u0431\u0440\u0430\u0437\u0438\u0435 \u2014 \u0446\u0435\u043D\u0442\u0440\u0430\u043B\u044C\u043D\u044B\u0439 \u043E\u0431\u044A\u0435\u043A\u0442 \u0438\u0437\u0443\u0447\u0435\u043D\u0438\u044F \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u043E\u0439 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0438. \u041A\u043B\u0430\u0441\u0441\u0438\u0447\u0435\u0441\u043A\u043E\u0435 \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u043D\u0438\u0435 \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u043E\u0433\u043E \u043C\u043D\u043E\u0433\u043E\u043E\u0431\u0440\u0430\u0437\u0438\u044F \u2014 \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u043E \u0440\u0435\u0448\u0435\u043D\u0438\u0439 \u0441\u0438\u0441\u0442\u0435\u043C\u044B \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u0438\u0445 \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u0439 \u043D\u0430\u0434 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043B\u044C\u043D\u044B\u043C\u0438 \u0438\u043B\u0438 \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u044B\u043C\u0438 \u0447\u0438\u0441\u043B\u0430\u043C\u0438. \u0421\u043E\u0432\u0440\u0435\u043C\u0435\u043D\u043D\u044B\u0435 \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u043D\u0438\u044F \u043E\u0431\u043E\u0431\u0449\u0430\u044E\u0442 \u0435\u0433\u043E \u0440\u0430\u0437\u043B\u0438\u0447\u043D\u044B\u043C\u0438 \u0441\u043F\u043E\u0441\u043E\u0431\u0430\u043C\u0438, \u043D\u043E \u0441\u0442\u0430\u0440\u0430\u044E\u0442\u0441\u044F \u0441\u043E\u0445\u0440\u0430\u043D\u0438\u0442\u044C \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043A\u0443\u044E \u0438\u043D\u0442\u0443\u0438\u0446\u0438\u044E, \u0441\u043E\u043E\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044E\u0449\u0443\u044E \u044D\u0442\u043E\u043C\u0443 \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u043D\u0438\u044E."@ru , "Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers. Modern definitions generalize this concept in several different ways, while attempting to preserve the geometric intuition behind the original definition. In the context of modern scheme theory, an algebraic variety over a field is an integral (irreducible and reduced) scheme over that field whose structure morphism is separated and of finite type."@en , "\u4EE3\u6570\u7C07\uFF0C\u4EA6\u4F5C\u4EE3\u6578\u591A\u6A23\u9AD4\uFF0C\u662F\u4EE3\u6570\u51E0\u4F55\u5B66\u4E0A\u591A\u9879\u5F0F\u96C6\u5408\u7684\u516C\u5171\u96F6\u70B9\u89E3\u7684\u96C6\u5408\u3002\u4EE3\u6570\u7C07\u662F\u7ECF\u5178\uFF08\u67D0\u79CD\u7A0B\u5EA6\u4E0A\u4E5F\u662F\u73B0\u4EE3\uFF09\u4EE3\u6570\u51E0\u4F55\u7684\u4E2D\u5FC3\u7814\u7A76\u5BF9\u8C61\u3002 \u8853\u8A9E\u7C07\uFF08variety\uFF09\u53D6\u81EA\u62C9\u4E01\u8BED\u65CF\u4E2D\u8A5E\u6E90\uFF08cognate of word\uFF09\u7684\u6982\u5FF5\uFF0C\u6709\u57FA\u65BC\u201C\u540C\u6E90\u201D\u800C\u201C\u8B8A\u5F62\u201D\u4E4B\u610F\u3002 \u5386\u53F2\u4E0A\uFF0C\u4EE3\u6570\u57FA\u672C\u5B9A\u7406\u5EFA\u7ACB\u4E86\u4EE3\u6570\u548C\u51E0\u4F55\u4E4B\u95F4\u7684\u4E00\u4E2A\u8054\u7CFB\uFF0C\u5B83\u8868\u660E\u5728\u590D\u6570\u57DF\u4E0A\u7684\u5355\u53D8\u91CF\u7684\u591A\u9879\u5F0F\u7531\u5B83\u7684\u6839\u7684\u96C6\u5408\u51B3\u5B9A\uFF0C\u800C\u6839\u96C6\u5408\u662F\u5185\u5728\u7684\u51E0\u4F55\u5BF9\u8C61\u3002\u5728\u6B64\u57FA\u7840\u4E0A\uFF0C\u5E0C\u5C14\u4F2F\u7279\u96F6\u70B9\u5B9A\u7406\u63D0\u4F9B\u4E86\u591A\u9879\u5F0F\u73AF\u7684\u7406\u60F3\u548C\u4EFF\u5C04\u7A7A\u95F4\u5B50\u96C6\u7684\u57FA\u672C\u5BF9\u5E94\u3002\u5229\u7528\u96F6\u70B9\u5B9A\u7406\u548C\u76F8\u5173\u7ED3\u679C\uFF0C\u6211\u4EEC\u80FD\u591F\u7528\u4EE3\u6570\u672F\u8BED\u6355\u6349\u7C07\u7684\u51E0\u4F55\u6982\u5FF5\uFF0C\u4E5F\u80FD\u591F\u7528\u51E0\u4F55\u6765\u627F\u8F7D\u73AF\u8BBA\u4E2D\u7684\u95EE\u9898\u3002"@zh , "\u4EE3\u6570\u591A\u69D8\u4F53\uFF08\u3060\u3044\u3059\u3046\u305F\u3088\u3046\u305F\u3044\u3001algebraic variety\uFF09\u306F\u3001\u6700\u3082\u7C21\u7565\u306B\u8A00\u3048\u3070\u3001\u591A\u5909\u6570\u591A\u9805\u5F0F\u304B\u3089\u306A\u308B\u9023\u7ACB\u65B9\u7A0B\u5F0F\u306E\u89E3\u96C6\u5408\u3068\u3057\u3066\u5B9A\u7FA9\u3055\u308C\u308B\u56F3\u5F62\u3067\u3042\u308B\u3002\u4EE3\u6570\u5E7E\u4F55\u5B66\u306E\u6700\u3082\u4E3B\u8981\u306A\u7814\u7A76\u5BFE\u8C61\u3067\u3042\u308A\u3001\u30C7\u30AB\u30EB\u30C8\u306B\u3088\u308B\u5EA7\u6A19\u5E73\u9762\u4E0A\u306E\u89E3\u6790\u5E7E\u4F55\u5B66\u306E\u5C0E\u5165\u4EE5\u6765\u3001\u591A\u304F\u306E\u6570\u5B66\u8005\u304C\u7814\u7A76\u3057\u3066\u304D\u305F\u6570\u5B66\u7684\u5BFE\u8C61\u3067\u3042\u308B\u3002\u4E3B\u306B\u306B\u3088\u308B\u5C04\u5F71\u5E7E\u4F55\u5B66\u7684\u4EE3\u6570\u591A\u69D8\u4F53\u3001\u304A\u3088\u3073\u305D\u306E\u9AD8\u6B21\u5143\u5316\u306B\u5F53\u305F\u308B\u30B6\u30EA\u30B9\u30AD\u304A\u3088\u3073\u30F4\u30A7\u30A4\u30E6\u306B\u3088\u308B\u4ED8\u5024\u8AD6\u7684\u62BD\u8C61\u4EE3\u6570\u591A\u69D8\u4F53\u306A\u3069\u306E\u57FA\u790E\u4ED8\u3051\u304C\u3042\u305F\u3048\u3089\u308C\u305F\u304C\u300120\u4E16\u7D00\u5F8C\u534A\u4EE5\u964D\u306F\u3088\u308A\u591A\u69D8\u4F53\u8AD6\u7684\u306A\u89B3\u70B9\u306B\u7ACB\u811A\u3057\u305F\u30B9\u30AD\u30FC\u30E0\u8AD6\u306B\u3088\u308B\u57FA\u790E\u4ED8\u3051\u3092\u7528\u3044\u308B\u306E\u304C\u901A\u5E38\u3067\u3042\u308B\u3002 \u672C\u9805\u3067\u306F\u3001\u30B9\u30AD\u30FC\u30E0\u8AD6\u7684\u306A\u89B3\u70B9\u306B\u7ACB\u3061\u3064\u3064\u3001\u30B9\u30AD\u30FC\u30E0\u8AD6\u3092\u76F4\u63A5\u7528\u3044\u305A\u4EE3\u6570\u591A\u69D8\u4F53\u3092\u5B9A\u7FA9\u3057\u305D\u306E\u6027\u8CEA\u306B\u3064\u3044\u3066\u8FF0\u3079\u308B\u3002\u307E\u305F\u8B70\u8AD6\u3092\u7C21\u6F54\u306B\u3059\u308B\u306E\u305F\u3081\u7279\u306B\u65AD\u3089\u306A\u3044\u9650\u308A\u4F53 k \u306F\u4EE3\u6570\u7684\u9589\u4F53\u3067\u3042\u308B\u3068\u4EEE\u5B9A\u3059\u308B\uFF08\u4F53 k \u304C\u4EE3\u6570\u7684\u9589\u3067\u3042\u308B\u3068\u3044\u3046\u6761\u4EF6\u3092\u9664\u53BB\u3059\u308B\u305F\u3081\u306B\u5FC5\u8981\u306A\u8003\u5BDF\u306B\u3064\u3044\u3066\u306F\u3092\u53C2\u7167\uFF09\u3002"@ja , "\u0412 \u0430\u043B\u0433\u0435\u0431\u0440\u0438\u0447\u043D\u0456\u0439 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0456\u0457 \u0430\u043B\u0433\u0435\u0431\u0440\u0438\u0447\u043D\u0438\u0439 \u043C\u043D\u043E\u0433\u043E\u0432\u0438\u0434 \u2014 \u043C\u043D\u043E\u0436\u0438\u043D\u0430 \u0442\u043E\u0447\u043E\u043A, \u043A\u043E\u043E\u0440\u0434\u0438\u043D\u0430\u0442\u0438 \u044F\u043A\u0438\u0445 \u0437\u0430\u0434\u043E\u0432\u043E\u043B\u044C\u043D\u044F\u044E\u0442\u044C \u0434\u0435\u044F\u043A\u0456\u0439 \u0441\u0438\u0441\u0442\u0435\u043C\u0456 \u043F\u043E\u043B\u0456\u043D\u043E\u043C\u0456\u0430\u043B\u044C\u043D\u0438\u0445 \u0440\u0456\u0432\u043D\u044F\u043D\u044C."@uk , "Inom matematiken \u00E4r en algebraisk varietet ett geometriskt objekt som lokalt definieras av polynomekvationer."@sv , "\u0641\u064A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A\u060C \u0627\u0644\u0645\u062C\u0645\u0648\u0639\u0629 \u0627\u0644\u062C\u0628\u0631\u064A\u0629 \u0647\u064A \u0645\u062C\u0645\u0648\u0639\u0629 \u062D\u0644\u0648\u0644 \u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u0645\u0639\u0627\u062F\u0644\u0627\u062A \u0627\u0644\u062C\u0628\u0631\u064A\u0629 \u0645\u062A\u0639\u062F\u062F\u0629 \u0627\u0644\u062D\u062F\u0648\u062F. \u0623\u062D\u064A\u0627\u0646\u064B\u0627 \u062A\u064F\u0639\u0631\u0641 \u0627\u0644\u0645\u062C\u0645\u0648\u0639\u0627\u062A \u0627\u0644\u062C\u0628\u0631\u064A\u0629 \u0628\u0627\u0644\u062A\u0646\u0648\u0639\u0627\u062A \u0627\u0644\u062C\u0628\u0631\u064A\u0629\u060C \u0644\u0643\u0646 \u0639\u0627\u062F\u0629\u064B \u064A\u064F\u0639\u0631\u0641 \u0627\u0644\u062A\u0646\u0648\u0639 \u0627\u0644\u062C\u0628\u0631\u064A \u0643\u0645\u062C\u0645\u0648\u0639\u0629 \u062C\u0628\u0631\u064A\u0629 \u063A\u064A\u0631 \u0642\u0627\u0628\u0644\u0629 \u0644\u0644\u062A\u062D\u0644\u064A\u0644\u060C \u0628\u0645\u0639\u0646\u0649 \u0623\u0646 \u0627\u0644\u0645\u062C\u0645\u0648\u0639\u0629 \u0627\u0644\u062C\u0628\u0631\u064A\u0629 \u0627\u0644\u0648\u0627\u062D\u062F\u0629 \u0644\u064A\u0633\u062A \u0646\u062A\u0627\u062C \u0627\u062A\u062D\u0627\u062F \u0645\u062C\u0645\u0648\u0639\u0627\u062A \u062C\u0628\u0631\u064A\u0629 \u0623\u062E\u0631\u0649. \u062A\u0646\u062F\u0631\u062C \u062F\u0631\u0627\u0633\u0629 \u0627\u0644\u0645\u062C\u0645\u0648\u0639\u0627\u062A \u0627\u0644\u062C\u0628\u0631\u064A\u0629 \u0648\u0627\u0644\u062A\u0646\u0648\u0639\u0627\u062A \u0627\u0644\u062C\u0628\u0631\u064A\u0629 \u062A\u062D\u062A \u0641\u0631\u0639 \u0647\u0627\u0645 \u0645\u0646 \u0641\u0631\u0648\u0639 \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A \u0648\u0647\u0648 \u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u062C\u0628\u0631\u064A\u0629."@ar , "En algebra geometrio, algebra varia\u0135o, a\u016D simple varia\u0135o, estas skemo, kiu estas loke izomorfa al la nulejo de prima idealo de polinomoj."@eo , "Una variet\u00E0 algebrica \u00E8 l'insieme degli zeri di una famiglia di polinomi, e costituisce l'oggetto principale di studio della geometria algebrica. Tramite il concetto di variet\u00E0 algebrica \u00E8 possibile costituire un legame tra l'algebra e la geometria, che permette di riformulare problemi geometrici in termini algebrici, e viceversa. Tale legame \u00E8 basato principalmente sul fatto che un polinomio complesso in una variabile \u00E8 completamente determinato dai suoi zeri: il teorema degli zeri di Hilbert permette infatti di stabilire una corrispondenza tra variet\u00E0 algebriche e ideali di anelli di polinomi."@it , "Algebraick\u00E1 varieta je matematick\u00FD pojem z oboru algebraick\u00E9 geometrie. Naz\u00FDv\u00E1 se tak mno\u017Eina v\u0161ech soustavy polynomi\u00E1ln\u00EDch rovnic \u2026"@cs , "Rozmaito\u015B\u0107 algebraiczna \u2013 zbi\u00F3r punkt\u00F3w, kt\u00F3rych wsp\u00F3\u0142rz\u0119dne spe\u0142niaj\u0105 pewien uk\u0142ad r\u00F3wna\u0144 wielomianowych. Historyczne znaczenie rozmaito\u015Bci algebraicznych zacz\u0119\u0142o by\u0107 widoczne od czasu udowodnienia podstawowego twierdzenia algebry, kt\u00F3re \u0142\u0105czy w pewnym sensie algebr\u0119 i geometri\u0119, gdy\u017C m\u00F3wi, \u017Ce wielomian jednej zmiennej zespolonej jest wyznaczony jednoznacznie przez zbi\u00F3r swoich pierwiastk\u00F3w \u2013 obiekt zasadniczo geometryczny. Rozszerzaj\u0105c to rozumowanie, twierdzenie Hilberta o zerach pokazuje fundamentaln\u0105 odpowiednio\u015B\u0107 mi\u0119dzy idea\u0142ami w pier\u015Bcieniach wielomian\u00F3w, a podzbiorami przestrzeni afinicznej. Dzi\u0119ki temu twierdzeniu i zwi\u0105zanym z nim wynikom, mo\u017Cemy bada\u0107 obiekty geometryczne, jakimi s\u0105 rozmaito\u015Bci algebraiczne, metodami algebry, w szczeg\u00F3lno\u015Bci teorii pier\u015Bcieni."@pl , "En geometr\u00EDa algebraica, una variedad algebraica es esencialmente un conjunto de puntos (finito o infinito) en los cuales un polinomio (de una o m\u00E1s variables) toma un valor cero, o en el cual un conjunto de tales polinomios toma un valor cero. Las variedades algebraicas son uno de los objetos centrales de estudio de la geometr\u00EDa algebraica cl\u00E1sica (y en ciertos aspectos moderna)."@es , "\u039F\u03B9 \u03B1\u03BB\u03B3\u03B5\u03B2\u03C1\u03B9\u03BA\u03AD\u03C2 \u03C0\u03BF\u03B9\u03BA\u03B9\u03BB\u03AF\u03B5\u03C2 \u03B5\u03AF\u03BD\u03B1\u03B9 \u03C4\u03BF \u03BA\u03B5\u03BD\u03C4\u03C1\u03B9\u03BA\u03CC \u03B1\u03BD\u03C4\u03B9\u03BA\u03B5\u03AF\u03BC\u03B5\u03BD\u03BF \u03BC\u03B5\u03BB\u03AD\u03C4\u03B7\u03C2 \u03C3\u03C4\u03B7\u03BD \u03B1\u03BB\u03B3\u03B5\u03B2\u03C1\u03B9\u03BA\u03AE \u03B3\u03B5\u03C9\u03BC\u03B5\u03C4\u03C1\u03AF\u03B1. \u039A\u03BB\u03B1\u03C3\u03C3\u03B9\u03BA\u03AC, \u03BC\u03B9\u03B1 \u03B1\u03BB\u03B3\u03B5\u03B2\u03C1\u03B9\u03BA\u03AE \u03C0\u03BF\u03B9\u03BA\u03B9\u03BB\u03AF\u03B1 \u03BF\u03C1\u03AF\u03B6\u03B5\u03C4\u03B1\u03B9 \u03C9\u03C2 \u03B5\u03BD\u03CC\u03C2 \u03C0\u03AC\u03BD\u03C9 \u03C3\u03C4\u03BF \u03C0\u03C1\u03B1\u03B3\u03BC\u03B1\u03C4\u03B9\u03BA\u03CC \u03B5\u03C0\u03AF\u03C0\u03B5\u03B4\u03BF \u03AE \u03BC\u03B9\u03B3\u03B1\u03B4\u03B9\u03BA\u03CC \u03B5\u03C0\u03AF\u03C0\u03B5\u03B4\u03BF. \u039C\u03BF\u03BD\u03C4\u03AD\u03C1\u03BD\u03BF\u03B9 \u03BF\u03C1\u03B9\u03C3\u03BC\u03BF\u03AF \u03B3\u03B5\u03BD\u03B9\u03BA\u03B5\u03CD\u03BF\u03C5\u03BD \u03B1\u03C5\u03C4\u03AE \u03C4\u03B7\u03BD \u03AD\u03BD\u03BD\u03BF\u03B9\u03B1 \u03BC\u03B5 \u03C0\u03BF\u03BB\u03BB\u03BF\u03CD\u03C2 \u03B4\u03B9\u03B1\u03C6\u03BF\u03C1\u03B5\u03C4\u03B9\u03BA\u03BF\u03CD\u03C2 \u03C4\u03C1\u03CC\u03C0\u03BF\u03C5\u03C2, \u03B5\u03BD\u03CE \u03C4\u03B1\u03C5\u03C4\u03CC\u03C7\u03C1\u03BF\u03BD\u03B1 \u03C0\u03C1\u03BF\u03C3\u03C0\u03B1\u03B8\u03B5\u03AF \u03BD\u03B1 \u03B4\u03B9\u03B1\u03C4\u03B7\u03C1\u03AE\u03C3\u03B5\u03B9 \u03C4\u03B7\u03BD \u03B3\u03B5\u03C9\u03BC\u03B5\u03C4\u03C1\u03B9\u03BA\u03AE \u03B4\u03B9\u03B1\u03AF\u03C3\u03B8\u03B7\u03C3\u03B7 \u03C0\u03AF\u03C3\u03C9 \u03B1\u03C0\u03CC \u03C4\u03BF\u03BD \u03B1\u03C1\u03C7\u03B9\u03BA\u03CC \u03BF\u03C1\u03B9\u03C3\u03BC\u03CC. \u0397 \u03AD\u03BD\u03BD\u03BF\u03B9\u03B1 \u03C4\u03B7\u03C2 \u03B1\u03BB\u03B3\u03B5\u03B2\u03C1\u03B9\u03BA\u03AE\u03C2 \u03C0\u03BF\u03B9\u03BA\u03B9\u03BB\u03AF\u03B1\u03C2 \u03B5\u03AF\u03BD\u03B1\u03B9 \u03C0\u03B1\u03C1\u03CC\u03BC\u03BF\u03B9\u03B1 \u03BC\u03B5 \u03B5\u03BA\u03B5\u03AF\u03BD\u03B7 \u03C4\u03B7\u03C2 \u03B1\u03BD\u03B1\u03BB\u03C5\u03C4\u03B9\u03BA\u03AE \u03C0\u03BF\u03BB\u03BB\u03B1\u03C0\u03BB\u03CC\u03C4\u03B7\u03C4\u03B1\u03C2. \u039C\u03B9\u03B1 \u03C3\u03B7\u03BC\u03B1\u03BD\u03C4\u03B9\u03BA\u03AE \u03B4\u03B9\u03B1\u03C6\u03BF\u03C1\u03AC \u03B5\u03AF\u03BD\u03B1\u03B9 \u03CC\u03C4\u03B9 \u03B7 \u03B1\u03BB\u03B3\u03B5\u03B2\u03C1\u03B9\u03BA\u03AE \u03C0\u03BF\u03B9\u03BA\u03B9\u03BB\u03AF\u03B1 \u03BC\u03C0\u03BF\u03C1\u03B5\u03AF \u03BD\u03B1 \u03AD\u03C7\u03B5\u03B9 \u03BC\u03B5\u03BC\u03BF\u03BD\u03C9\u03BC\u03AD\u03BD\u03B1 \u03C3\u03B7\u03BC\u03B5\u03AF\u03B1 \u03B5\u03BD\u03CE \u03C3\u03C4\u03B7\u03BD \u03B1\u03BD\u03B1\u03BB\u03C5\u03C4\u03B9\u03BA\u03AE \u03C0\u03BF\u03BB\u03BB\u03B1\u03C0\u03BB\u03CC\u03C4\u03B7\u03C4\u03B1 \u03BA\u03AC\u03C4\u03B9 \u03C4\u03AD\u03C4\u03BF\u03B9\u03BF \u03B4\u03B5\u03BD \u03B5\u03AF\u03BD\u03B1\u03B9 \u03B5\u03C6\u03B9\u03BA\u03C4\u03CC."@el , "In der klassischen algebraischen Geometrie, einem Teilgebiet der Mathematik, ist eine algebraische Variet\u00E4t ein geometrisches Objekt, das durch Polynomgleichungen beschrieben werden kann."@de , "Di matematika, varietas aljabar adalah dari sistem persamaan . Varietas aljabar seperti manifold, juga objek geometri, tetapi objek itu didefininsikan menurut sebuah tempat kedudukan yang digambarkan menggunakan sebuah persamaan aljabar. Titik-titik yang memenuhi persamaan membentuk sebuah lingkaran dalam sebuah bidang datar. Dalam bahasa sehari-hari, yang dimaksudkan oleh Nash bahwa untuk setiap manifold pasti ada sebuah varietas aljabar yang bagiannnya berhubungan erat dengan objek aslinya."@in , "En matem\u00E0tiques, una varietat algebraica \u00E9s essencialment un conjunt de zeros comuns d'un conjunt de polinomis. Les varietats algebraiques s\u00F3n un dels objectes centrals de l'estudi en la geometria algebraica cl\u00E0ssica (i esteses, tamb\u00E9 en la moderna). El concepte de varietat algebraica \u00E9s similar al de varietat. Una difer\u00E8ncia important \u00E9s que una varietat algebraica pot tenir punts singulars, mentre que una varietat no en pot tenir."@ca , "Uma variedade alg\u00E9brica \u00E9 o conjunto de zeros de uma fam\u00EDlia de polin\u00F4mios, e constitui o objeto principal de estudo da geometria alg\u00E9brica. Pelo conceito de variedade alg\u00E9brica \u00E9 poss\u00EDvel constituir uma rela\u00E7\u00E3o entre a \u00E1lgebra e a geometria, que permite se reformular problemas geom\u00E9tricos em termos alg\u00E9bricos, e vice-versa. Tal rela\u00E7\u00E3o \u00E9 baseada principalmente no fato que um polin\u00F4mio complexo em uma vari\u00E1vel \u00E9 completamente determinado em seus zeros: o teorema dos zeros de Hilbert permite de fato estabelecer-se uma correspond\u00EAncia entre variedade alg\u00E9brica e ideal de an\u00E9is de polin\u00F4mios."@pt , "Une vari\u00E9t\u00E9 alg\u00E9brique est, de mani\u00E8re informelle, l'ensemble des racines communes d'un nombre fini de polyn\u00F4mes en plusieurs ind\u00E9termin\u00E9es. C'est l'objet d'\u00E9tude de la g\u00E9om\u00E9trie alg\u00E9brique. Les sch\u00E9mas sont des g\u00E9n\u00E9ralisations des vari\u00E9t\u00E9s alg\u00E9briques. Il y a deux points de vue (essentiellement \u00E9quivalents) sur les vari\u00E9t\u00E9s alg\u00E9briques : elles peuvent \u00EAtre d\u00E9finies comme des sch\u00E9mas de type fini sur un corps (langage de Grothendieck), ou bien comme la restriction d'un tel sch\u00E9ma au sous-ensemble des points ferm\u00E9s. On utilise ici le deuxi\u00E8me point de vue, plus classique."@fr , "In de algebra\u00EFsche meetkunde, een deelgebied van de wiskunde, is een algebra\u00EFsche vari\u00EBteit de oplossingsverzameling van een systeem van polynomiale vergelijkingen. Algebra\u00EFsche vari\u00EBteiten zijn de fundamentele objecten in de klassieke (en tot op zekere hoogte, moderne) algebra\u00EFsche meetkunde."@nl ; rdfs:seeAlso dbr:Morphism_of_varieties . @prefix foaf: . dbr:Algebraic_variety foaf:depiction , . @prefix dcterms: . @prefix dbc: . dbr:Algebraic_variety dcterms:subject dbc:Algebraic_varieties , dbc:Algebraic_geometry ; dbo:wikiPageID 248808 ; dbo:wikiPageRevisionID 1124702772 ; dbo:wikiPageWikiLink dbr:Polynomial_factorization , dbr:Closed_immersion , dbr:Natural_topology , dbr:Structure_sheaf , , dbr:Masayoshi_Nagata , , dbr:Toric_variety , dbr:Closed_set , , , dbr:Absolutely_irreducible , dbr:Hypersurface , dbr:Manifold , dbr:Proj_construction , dbr:Subset , , dbr:Zariski_topology , dbr:Genus_formula , , dbr:If_and_only_if , dbr:Monic_polynomial , , dbr:Siegel_modular_form , , dbr:Linear_algebraic_group , dbr:Geometric_invariant_theory , dbr:Homogeneous_polynomials , , dbr:Regular_function , dbr:Analytic_variety , , dbr:Moduli_of_curves , dbr:Projective_line , dbr:Tautological_bundle , , dbr:Springer-Verlag , dbr:Locally_free_sheaf , dbr:Geometry , dbr:Mathematics , dbr:Complete_variety , dbr:Twisted_cubic , dbr:Nash_manifold , , dbr:System_of_polynomial_equations , dbr:Singular_point_of_an_algebraic_variety , dbr:Function_field_of_an_algebraic_variety , dbr:Riemann_sphere , dbr:Jean-Pierre_Serre , , dbr:Projective_variety , dbr:Chern_class , dbr:Foundations_of_Algebraic_Geometry , , dbr:Dimension_of_an_algebraic_variety , dbr:Zero_of_a_function , dbr:Minimal_compactification , dbr:Exterior_power , dbr:Monomial_order , dbr:Homogeneous_coordinate_ring , dbr:Homogeneous_coordinates , , dbr:Segre_embedding , dbr:Homogeneous_polynomial , dbr:Affine_space , dbr:Natural_number , dbr:Vector_bundle , dbr:Divisor_class_group , dbr:Projective_space , dbr:Semi-algebraic_set , dbr:Real_number , dbr:Affine_coordinate_system , , , dbr:Ring_theory , dbr:Determinant_of_a_matrix , dbr:Smooth_function , dbr:Solution_set , dbr:Modular_form , dbr:Characteristic_class , , dbr:Nilradical_of_a_ring , dbr:Fiber_product_of_schemes , dbr:Moduli_stack , dbr:Unit_circle , dbr:Veronese_embedding , dbr:Glossary_of_scheme_theory , dbr:Complex_number , dbr:Fundamental_theorem_of_algebra , dbr:Graph_isomorphism , , dbr:Algebra , dbr:Nilpotent , dbr:Grassmannian_variety , dbr:Quasi-projective_variety , dbr:Injective_function , , dbr:Complex_plane , dbr:Abelian_group , dbr:Identity_function , dbr:Algebraic_geometry_of_projective_spaces , dbc:Algebraic_varieties , dbr:Abelian_variety , dbr:Polynomial_ring , , dbr:Generic_property , , dbr:Picard_group , dbr:Quotient_ring , dbr:Algebraic_curve , dbr:Quasiprojective_variety , , dbr:Prime_ideal , , dbr:Algebraic_geometry , dbr:Algebraic_space , dbr:Algebraic_stack , dbr:Jacobian_variety , dbr:Algebraic_surface , dbc:Algebraic_geometry , dbr:Toroidal_compactification , dbr:Moduli_of_algebraic_curves , dbr:Projective_algebraic_manifold , dbr:Unitary_group , dbr:Structure_morphism , dbr:Algebraic_torus , dbr:Algebraically_closed_field , , dbr:Algebraic_variety , dbr:Alexander_Grothendieck , dbr:Birational_geometry , dbr:Finite_morphism , dbr:Vector_space , dbr:Polynomial_algebra , dbr:Stable_curve , dbr:Locally_ringed_space , dbr:Spectrum_of_a_ring , dbr:Sheaf_cohomology , dbr:Elliptic_curve , dbr:Stable_vector_bundle , dbr:Integral_domain , dbr:Claude_Chevalley , dbr:Theta_function , dbr:General_linear_group ; dbo:wikiPageExternalLink , , ; owl:sameAs , , . @prefix dbpedia-simple: . dbr:Algebraic_variety owl:sameAs dbpedia-simple:Algebraic_variety , . @prefix dbpedia-sr: . dbr:Algebraic_variety owl:sameAs dbpedia-sr:Algebarski_varijeteti , , , . @prefix dbpedia-et: . dbr:Algebraic_variety owl:sameAs dbpedia-et:Algebraline_muutkond , , , , . @prefix wikidata: . dbr:Algebraic_variety owl:sameAs wikidata:Q648995 , , . @prefix yago-res: . dbr:Algebraic_variety owl:sameAs yago-res:Algebraic_variety , , . @prefix dbpedia-id: . dbr:Algebraic_variety owl:sameAs dbpedia-id:Varietas_aljabar . @prefix dbpedia-sl: . dbr:Algebraic_variety owl:sameAs dbpedia-sl:Algebrska_varieteta , , , , , , , , , , . @prefix dbpedia-es: . dbr:Algebraic_variety owl:sameAs dbpedia-es:Variedad_algebraica , . @prefix dbpedia-sv: . dbr:Algebraic_variety owl:sameAs dbpedia-sv:Algebraisk_varietet . @prefix dbpedia-ca: . dbr:Algebraic_variety owl:sameAs dbpedia-ca:Varietat_algebraica , . @prefix dbp: . @prefix dbt: . dbr:Algebraic_variety dbp:wikiPageUsesTemplate dbt:See_also , dbt:Section_link , dbt:Short_description , dbt:Main , dbt:PlanetMath_attribution , dbt:Cite_book , dbt:Cite_web , dbt:R , dbt:Authority_control , dbt:Math , , dbt:Mvar , dbt:Reflist , dbt:No_footnotes , dbt:Refend , dbt:Refbegin , dbt:About , dbt:Sfnref ; dbo:thumbnail ; dbp:title "Isomorphism of varieties"@en ; dbp:urlname "isomorphismofvarieties"@en ; dbo:abstract "Una variet\u00E0 algebrica \u00E8 l'insieme degli zeri di una famiglia di polinomi, e costituisce l'oggetto principale di studio della geometria algebrica. Tramite il concetto di variet\u00E0 algebrica \u00E8 possibile costituire un legame tra l'algebra e la geometria, che permette di riformulare problemi geometrici in termini algebrici, e viceversa. Tale legame \u00E8 basato principalmente sul fatto che un polinomio complesso in una variabile \u00E8 completamente determinato dai suoi zeri: il teorema degli zeri di Hilbert permette infatti di stabilire una corrispondenza tra variet\u00E0 algebriche e ideali di anelli di polinomi."@it , "Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers. Modern definitions generalize this concept in several different ways, while attempting to preserve the geometric intuition behind the original definition. Conventions regarding the definition of an algebraic variety differ slightly. For example, some definitions require an algebraic variety to be irreducible, which means that it is not the union of two smaller sets that are closed in the Zariski topology. Under this definition, non-irreducible algebraic varieties are called algebraic sets. Other conventions do not require irreducibility. The fundamental theorem of algebra establishes a link between algebra and geometry by showing that a monic polynomial (an algebraic object) in one variable with complex number coefficients is determined by the set of its roots (a geometric object) in the complex plane. Generalizing this result, Hilbert's Nullstellensatz provides a fundamental correspondence between ideals of polynomial rings and algebraic sets. Using the Nullstellensatz and related results, mathematicians have established a strong correspondence between questions on algebraic sets and questions of ring theory. This correspondence is a defining feature of algebraic geometry. Many algebraic varieties are manifolds, but an algebraic variety may have singular points while a manifold cannot. Algebraic varieties can be characterized by their dimension. Algebraic varieties of dimension one are called algebraic curves and algebraic varieties of dimension two are called algebraic surfaces. In the context of modern scheme theory, an algebraic variety over a field is an integral (irreducible and reduced) scheme over that field whose structure morphism is separated and of finite type."@en , "En geometr\u00EDa algebraica, una variedad algebraica es esencialmente un conjunto de puntos (finito o infinito) en los cuales un polinomio (de una o m\u00E1s variables) toma un valor cero, o en el cual un conjunto de tales polinomios toma un valor cero. Las variedades algebraicas son uno de los objetos centrales de estudio de la geometr\u00EDa algebraica cl\u00E1sica (y en ciertos aspectos moderna). Desde un punto de vista hist\u00F3rico, el teorema fundamental del \u00E1lgebra estableci\u00F3 la relaci\u00F3n entre el \u00E1lgebra y la geometr\u00EDa al indicar que un polinomio de una variable en los n\u00FAmeros complejos queda determinado por su conjunto de ra\u00EDces, que es un objeto geom\u00E9trico inherente. Construyendo sobre este resultado, el Teorema de los ceros de Hilbert establece una correspondencia fundamental entre los ideales de los anillos de polinomios y los subconjuntos del espacio af\u00EDn. Utilizando el teorema de ceros y sus resultados asociados, es posible capturar la noci\u00F3n geom\u00E9trica de una variedad en t\u00E9rminos algebraicos como tambi\u00E9n hacer que la geometr\u00EDa entienda sobre temas de la teor\u00EDa de anillos."@es , "\u4EE3\u6570\u7C07\uFF0C\u4EA6\u4F5C\u4EE3\u6578\u591A\u6A23\u9AD4\uFF0C\u662F\u4EE3\u6570\u51E0\u4F55\u5B66\u4E0A\u591A\u9879\u5F0F\u96C6\u5408\u7684\u516C\u5171\u96F6\u70B9\u89E3\u7684\u96C6\u5408\u3002\u4EE3\u6570\u7C07\u662F\u7ECF\u5178\uFF08\u67D0\u79CD\u7A0B\u5EA6\u4E0A\u4E5F\u662F\u73B0\u4EE3\uFF09\u4EE3\u6570\u51E0\u4F55\u7684\u4E2D\u5FC3\u7814\u7A76\u5BF9\u8C61\u3002 \u8853\u8A9E\u7C07\uFF08variety\uFF09\u53D6\u81EA\u62C9\u4E01\u8BED\u65CF\u4E2D\u8A5E\u6E90\uFF08cognate of word\uFF09\u7684\u6982\u5FF5\uFF0C\u6709\u57FA\u65BC\u201C\u540C\u6E90\u201D\u800C\u201C\u8B8A\u5F62\u201D\u4E4B\u610F\u3002 \u5386\u53F2\u4E0A\uFF0C\u4EE3\u6570\u57FA\u672C\u5B9A\u7406\u5EFA\u7ACB\u4E86\u4EE3\u6570\u548C\u51E0\u4F55\u4E4B\u95F4\u7684\u4E00\u4E2A\u8054\u7CFB\uFF0C\u5B83\u8868\u660E\u5728\u590D\u6570\u57DF\u4E0A\u7684\u5355\u53D8\u91CF\u7684\u591A\u9879\u5F0F\u7531\u5B83\u7684\u6839\u7684\u96C6\u5408\u51B3\u5B9A\uFF0C\u800C\u6839\u96C6\u5408\u662F\u5185\u5728\u7684\u51E0\u4F55\u5BF9\u8C61\u3002\u5728\u6B64\u57FA\u7840\u4E0A\uFF0C\u5E0C\u5C14\u4F2F\u7279\u96F6\u70B9\u5B9A\u7406\u63D0\u4F9B\u4E86\u591A\u9879\u5F0F\u73AF\u7684\u7406\u60F3\u548C\u4EFF\u5C04\u7A7A\u95F4\u5B50\u96C6\u7684\u57FA\u672C\u5BF9\u5E94\u3002\u5229\u7528\u96F6\u70B9\u5B9A\u7406\u548C\u76F8\u5173\u7ED3\u679C\uFF0C\u6211\u4EEC\u80FD\u591F\u7528\u4EE3\u6570\u672F\u8BED\u6355\u6349\u7C07\u7684\u51E0\u4F55\u6982\u5FF5\uFF0C\u4E5F\u80FD\u591F\u7528\u51E0\u4F55\u6765\u627F\u8F7D\u73AF\u8BBA\u4E2D\u7684\u95EE\u9898\u3002"@zh , "In der klassischen algebraischen Geometrie, einem Teilgebiet der Mathematik, ist eine algebraische Variet\u00E4t ein geometrisches Objekt, das durch Polynomgleichungen beschrieben werden kann."@de , "In de algebra\u00EFsche meetkunde, een deelgebied van de wiskunde, is een algebra\u00EFsche vari\u00EBteit de oplossingsverzameling van een systeem van polynomiale vergelijkingen. Algebra\u00EFsche vari\u00EBteiten zijn de fundamentele objecten in de klassieke (en tot op zekere hoogte, moderne) algebra\u00EFsche meetkunde. Historisch gezien legt de hoofdstelling van de algebra een verband tussen de algebra en de meetkunde door aan te tonen dat een monomiale veelterm in \u00E9\u00E9n variabele over de complexe getallen, dus een algebra\u00EFsch object, wordt bepaald door een meetkundig object, namelijk de verzameling van haar nulpunten. Voortbouwend op dit resultaat legt Hilberts Nullstellensatz een fundamenteel verband tussen idealen van veeltermringen en deelverzamelingen van affiene ruimten. Met behulp van de Nullstellensatz en daaraan gerelateerde resultaten, is men in staat het meetkundige begrip vari\u00EBteit in algebra\u00EFsche termen te beschrijven, alsook de meetkunde in te schakelen om antwoorden te geven op vragen uit de ringtheorie."@nl , "Une vari\u00E9t\u00E9 alg\u00E9brique est, de mani\u00E8re informelle, l'ensemble des racines communes d'un nombre fini de polyn\u00F4mes en plusieurs ind\u00E9termin\u00E9es. C'est l'objet d'\u00E9tude de la g\u00E9om\u00E9trie alg\u00E9brique. Les sch\u00E9mas sont des g\u00E9n\u00E9ralisations des vari\u00E9t\u00E9s alg\u00E9briques. Il y a deux points de vue (essentiellement \u00E9quivalents) sur les vari\u00E9t\u00E9s alg\u00E9briques : elles peuvent \u00EAtre d\u00E9finies comme des sch\u00E9mas de type fini sur un corps (langage de Grothendieck), ou bien comme la restriction d'un tel sch\u00E9ma au sous-ensemble des points ferm\u00E9s. On utilise ici le deuxi\u00E8me point de vue, plus classique."@fr , "\u0410\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u043E\u0435 \u043C\u043D\u043E\u0433\u043E\u043E\u0431\u0440\u0430\u0437\u0438\u0435 \u2014 \u0446\u0435\u043D\u0442\u0440\u0430\u043B\u044C\u043D\u044B\u0439 \u043E\u0431\u044A\u0435\u043A\u0442 \u0438\u0437\u0443\u0447\u0435\u043D\u0438\u044F \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u043E\u0439 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0438. \u041A\u043B\u0430\u0441\u0441\u0438\u0447\u0435\u0441\u043A\u043E\u0435 \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u043D\u0438\u0435 \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u043E\u0433\u043E \u043C\u043D\u043E\u0433\u043E\u043E\u0431\u0440\u0430\u0437\u0438\u044F \u2014 \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u043E \u0440\u0435\u0448\u0435\u043D\u0438\u0439 \u0441\u0438\u0441\u0442\u0435\u043C\u044B 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\u0648\u0627\u062D\u062F\u064A\u0629 \u0627\u0644\u0645\u062F\u062E\u0644) \u0641\u064A \u0627\u0644\u0645\u062A\u063A\u064A\u0631 \u0627\u0644\u0648\u0627\u062D\u062F \u0645\u0639 \u0627\u0644\u0645\u0639\u0627\u0645\u0644\u0627\u062A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0629 \u0627\u0644\u0645\u0631\u0643\u0628\u0629 (\u0643\u0627\u0626\u0646 \u062C\u0628\u0631\u064A) \u064A\u062A\u0645 \u0627\u0644\u0644\u062C\u0648\u0621 \u0625\u0644\u0649 \u0645\u062C\u0645\u0648\u0639\u0629 \u0645\u0646 \u062C\u0630\u0648\u0631\u0647\u0627 \u0627\u0644\u062F\u0627\u0644\u0629 \u0627\u0644\u062A\u064A \u062A\u064F\u0639\u062F \u0641\u064A \u0627\u0644\u0623\u0635\u0644 (\u0643\u0627\u0626\u0646 \u0647\u0646\u062F\u0633\u064A). \u0645\u0639 \u062A\u0639\u0645\u064A\u0645 \u0647\u0630\u0647 \u0627\u0644\u0646\u062A\u064A\u062C\u0629\u060C \u062A\u0648\u0635\u0644 \u0639\u0627\u0644\u0645 \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A \u0627\u0644\u0623\u0644\u0645\u0627\u0646\u064A \u062F\u064A\u0641\u064A\u062F \u0647\u064A\u0644\u0628\u0631\u062A \u0641\u064A \u0645\u0628\u0631\u0647\u0646\u062A\u0647 \u0639\u0646 \u0645\u0639\u062F\u0644 \u0627\u0644\u0635\u0641\u0631 \u0627\u0644\u062A\u064A \u062A\u064F\u0639\u0631\u0641 \u0628\u0627\u0633\u0645 (Hilbert's Nullstellensatz) \u0625\u0644\u0649 \u0648\u062C\u0648\u062F \u0639\u0644\u0627\u0642\u0629 \u062C\u0648\u0647\u0631\u064A\u0629 \u0628\u064A\u0646 \u0627\u0644\u0645\u062C\u0645\u0648\u0639\u0627\u062A \u0627\u0644\u062C\u0632\u0626\u064A\u0629 \u0644\u0644\u062D\u0644\u0642\u0627\u062A \u0645\u062A\u0639\u062F\u062F\u0629 \u0627\u0644\u062D\u062F\u0648\u062F \u0648\u0627\u0644\u0645\u062C\u0645\u0648\u0639\u0627\u062A \u0627\u0644\u062C\u0628\u0631\u064A\u0629. \u0645\u0639 \u0627\u0633\u062A\u062E\u062F\u0627\u0645 \u0646\u062A\u064A\u062C\u0629 Nullstellensatz \u0627\u0644\u062A\u064A \u062A\u0648\u0635\u0644 \u0625\u0644\u064A\u0647\u0627 \u0647\u064A\u0644\u0628\u0631\u062A \u0648\u0646\u062A\u0627\u0626\u062C \u0623\u062E\u0631\u0649\u060C \u0627\u0633\u062A\u0637\u0627\u0639 \u0627\u0644\u0639\u062F\u064A\u062F \u0645\u0646 \u0639\u0644\u0645\u0627\u0621 \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A \u0625\u062B\u0628\u0627\u062A \u0648\u062C\u0648\u062F \u0639\u0644\u0627\u0642\u0629 \u0648\u062B\u064A\u0642\u0629 \u0628\u064A\u0646 \u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u0645\u062C\u0645\u0648\u0639\u0627\u062A \u0627\u0644\u062C\u0628\u0631\u064A\u0629 \u0648\u0645\u0633\u0627\u0626\u0644 \u0646\u0638\u0631\u064A\u0629 \u0627\u0644\u062D\u0644\u0642\u0627\u062A. \u062A\u064F\u0639\u062F \u0647\u0630\u0647 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0627\u0644\u0633\u0645\u0629 \u0627\u0644\u062A\u064A \u062A\u0645\u064A\u0632 \u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u062C\u0628\u0631\u064A\u0629 \u0639\u0646 \u0628\u0627\u0642\u064A \u0641\u0631\u0648\u0639 \u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0629 \u0627\u0644\u0623\u062E\u0631\u0649."@ar , "Uma variedade alg\u00E9brica \u00E9 o conjunto de zeros de uma fam\u00EDlia de polin\u00F4mios, e constitui o objeto principal de estudo da geometria alg\u00E9brica. Pelo conceito de variedade alg\u00E9brica \u00E9 poss\u00EDvel constituir uma rela\u00E7\u00E3o entre a \u00E1lgebra e a geometria, que permite se reformular problemas geom\u00E9tricos em termos alg\u00E9bricos, e vice-versa. Tal rela\u00E7\u00E3o \u00E9 baseada principalmente no fato que um polin\u00F4mio complexo em uma vari\u00E1vel \u00E9 completamente determinado em seus zeros: o teorema dos zeros de Hilbert permite de fato estabelecer-se uma correspond\u00EAncia entre variedade alg\u00E9brica e ideal de an\u00E9is de polin\u00F4mios."@pt , "\u4EE3\u6570\u591A\u69D8\u4F53\uFF08\u3060\u3044\u3059\u3046\u305F\u3088\u3046\u305F\u3044\u3001algebraic 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\u03B1\u03C1\u03B9\u03B8\u03BC\u03BF\u03CD\u03C2 \u03C3\u03C5\u03BD\u03C4\u03B5\u03BB\u03B5\u03C3\u03C4\u03AD\u03C2 \u03BA\u03B1\u03B8\u03BF\u03C1\u03AF\u03B6\u03B5\u03C4\u03B1\u03B9 \u03B1\u03C0\u03CC \u03C4\u03BF \u03C3\u03CD\u03BD\u03BF\u03BB\u03BF \u03C4\u03C9\u03BD \u03C1\u03B9\u03B6\u03CE\u03BD \u03C4\u03BF\u03C5 (\u03AD\u03BD\u03B1 \u03B3\u03B5\u03C9\u03BC\u03B5\u03C4\u03C1\u03B9\u03BA\u03CC \u03B1\u03BD\u03C4\u03B9\u03BA\u03B5\u03AF\u03BC\u03B5\u03BD\u03BF)\u03C3\u03C4\u03BF \u03BA\u03B1\u03C1\u03C4\u03B5\u03C3\u03B9\u03B1\u03BD\u03CC \u03B5\u03C0\u03AF\u03C0\u03B5\u03B4\u03BF. \u0393\u03B5\u03BD\u03B9\u03BA\u03B5\u03CD\u03BF\u03BD\u03C4\u03B1\u03C2 \u03B1\u03C5\u03C4\u03CC \u03C4\u03BF \u03B1\u03C0\u03BF\u03C4\u03AD\u03BB\u03B5\u03C3\u03BC\u03B1,\u03BF \u03C0\u03B1\u03C1\u03AD\u03C7\u03B5\u03B9 \u03BC\u03B9\u03B1 \u03B8\u03B5\u03BC\u03B5\u03BB\u03B9\u03CE\u03B4\u03B7 \u03B1\u03BB\u03BB\u03B7\u03BB\u03B5\u03C0\u03AF\u03B4\u03C1\u03B1\u03C3\u03B7 \u03BC\u03B5\u03C4\u03B1\u03BE\u03CD \u03C4\u03C9\u03BD \u03C5\u03C0\u03BF\u03C3\u03C5\u03BD\u03CC\u03BB\u03C9\u03BD \u03C4\u03C9\u03BD \u03C0\u03BF\u03BB\u03C5\u03C9\u03BD\u03C5\u03BC\u03B9\u03BA\u03CE\u03BD \u03B4\u03B1\u03BA\u03C4\u03C5\u03BB\u03AF\u03C9\u03BD \u03BA\u03B1\u03B9 \u03C4\u03C9\u03BD \u03B1\u03BB\u03B3\u03B5\u03B2\u03C1\u03B9\u03BA\u03CE\u03BD \u03C3\u03C5\u03BD\u03CC\u03BB\u03C9\u03BD. \u03A7\u03C1\u03B7\u03C3\u03B9\u03BC\u03BF\u03C0\u03BF\u03B9\u03CE\u03BD\u03C4\u03B1\u03C2 \u03C4\u03BF Nullstellensatz \u03BA\u03B1\u03B9 \u03C4\u03B1 \u03C3\u03C7\u03B5\u03C4\u03B9\u03BA\u03AC \u03B1\u03C0\u03BF\u03C4\u03B5\u03BB\u03AD\u03C3\u03BC\u03B1\u03C4\u03B1, \u03BF\u03B9 \u03BC\u03B1\u03B8\u03B7\u03BC\u03B1\u03C4\u03B9\u03BA\u03BF\u03AF \u03AD\u03C7\u03BF\u03C5\u03BD \u03BA\u03B1\u03B8\u03B9\u03B5\u03C1\u03CE\u03C3\u03B5\u03B9 \u03BC\u03B9\u03B1 \u03B9\u03C3\u03C7\u03C5\u03C1\u03AE \u03C3\u03CD\u03BD\u03B4\u03B5\u03C3\u03B7 \u03BC\u03B5\u03C4\u03B1\u03BE\u03CD \u03C4\u03C9\u03BD \u03B5\u03C1\u03C9\u03C4\u03AE\u03C3\u03B5\u03C9\u03BD \u03C3\u03C4\u03B1 \u03B1\u03BB\u03B3\u03B5\u03B2\u03C1\u03B9\u03BA\u03AC \u03C3\u03CD\u03BD\u03BF\u03BB\u03B1 \u03BA\u03B1\u03B9 \u03C4\u03C9\u03BD \u03B8\u03B5\u03BC\u03AC\u03C4\u03C9\u03BD \u03C4\u03B7\u03C2 \u03B8\u03B5\u03C9\u03C1\u03AF\u03B1\u03C2 \u03B4\u03B1\u03BA\u03C4\u03C5\u03BB\u03AF\u03C9\u03BD. \u0391\u03C5\u03C4\u03AE \u03B7 \u03C3\u03CD\u03BD\u03B4\u03B5\u03C3\u03B7 \u03B5\u03AF\u03BD\u03B1\u03B9 \u03B7 \u03B9\u03B4\u03B9\u03BF\u03BC\u03BF\u03C1\u03C6\u03AF\u03B1 \u03C4\u03B7\u03C2 \u03B1\u03BB\u03B3\u03B5\u03B2\u03C1\u03B9\u03BA\u03AE\u03C2 \u03B3\u03B5\u03C9\u03BC\u03B5\u03C4\u03C1\u03AF\u03B1\u03C2."@el , "Di matematika, varietas aljabar adalah dari sistem persamaan . Varietas aljabar seperti manifold, juga objek geometri, tetapi objek itu didefininsikan menurut sebuah tempat kedudukan yang digambarkan menggunakan sebuah persamaan aljabar. Titik-titik yang memenuhi persamaan membentuk sebuah lingkaran dalam sebuah bidang datar. Dalam bahasa sehari-hari, yang dimaksudkan oleh Nash bahwa untuk setiap manifold pasti ada sebuah varietas aljabar yang bagiannnya berhubungan erat dengan objek aslinya."@in , "Rozmaito\u015B\u0107 algebraiczna \u2013 zbi\u00F3r punkt\u00F3w, kt\u00F3rych wsp\u00F3\u0142rz\u0119dne spe\u0142niaj\u0105 pewien uk\u0142ad r\u00F3wna\u0144 wielomianowych. Historyczne znaczenie rozmaito\u015Bci algebraicznych zacz\u0119\u0142o by\u0107 widoczne od czasu udowodnienia podstawowego twierdzenia algebry, kt\u00F3re \u0142\u0105czy w pewnym sensie algebr\u0119 i geometri\u0119, gdy\u017C m\u00F3wi, \u017Ce wielomian jednej zmiennej zespolonej jest wyznaczony jednoznacznie przez zbi\u00F3r swoich pierwiastk\u00F3w \u2013 obiekt zasadniczo geometryczny. Rozszerzaj\u0105c to rozumowanie, twierdzenie Hilberta o zerach pokazuje fundamentaln\u0105 odpowiednio\u015B\u0107 mi\u0119dzy idea\u0142ami w pier\u015Bcieniach wielomian\u00F3w, a podzbiorami przestrzeni afinicznej. Dzi\u0119ki temu twierdzeniu i zwi\u0105zanym z nim wynikom, mo\u017Cemy bada\u0107 obiekty geometryczne, jakimi s\u0105 rozmaito\u015Bci algebraiczne, metodami algebry, w szczeg\u00F3lno\u015Bci teorii pier\u015Bcieni."@pl , "En algebra geometrio, algebra varia\u0135o, a\u016D simple varia\u0135o, estas skemo, kiu estas loke izomorfa al la nulejo de prima idealo de polinomoj."@eo , "En matem\u00E0tiques, una varietat algebraica \u00E9s essencialment un conjunt de zeros comuns d'un conjunt de polinomis. Les varietats algebraiques s\u00F3n un dels objectes centrals de l'estudi en la geometria algebraica cl\u00E0ssica (i esteses, tamb\u00E9 en la moderna). Existeixen diferents convencions sobre la definici\u00F3 de varietat algebraica, que difereixen lleugerament entre si. Per exemple, algunes definicions exigeixen que la varietat algebraica sigui irreductible, la qual cosa vol dir que no sigui la uni\u00F3 de dos conjunts m\u00E9s petits que siguin tancats per la . Amb aquesta definici\u00F3, les varietats algebraiques no irreductibles s'anomenen conjunts algebraics. Altres convencions no requereixen la irreductibilitat. El concepte de varietat algebraica \u00E9s similar al de varietat. Una difer\u00E8ncia important \u00E9s que una varietat algebraica pot tenir punts singulars, mentre que una varietat no en pot tenir. El teorema fonamental de l'\u00E0lgebra estableix una connexi\u00F3 entre l'\u00E0lgebra i la geometria, mostrant que un polinomi m\u00F2nic (un objecte algebraic) en una variable amb coeficients complexos est\u00E0 determinat pel conjunt de les seves arrels (un objecte geom\u00E8tric) en el pla complex. Com a generalitzaci\u00F3 d'aquest resultat, el teorema dels zeros de Hilbert (Nullstellensatz) proporciona una correspond\u00E8ncia fonamental entre els ideals dels anells de polinomis i els conjunts algebraics. Amb la utilitzaci\u00F3 del Nullstellensatz i altres resultats relacionats, els matem\u00E0tics han establert una forta correspond\u00E8ncia entre q\u00FCestions sobre conjunts algebraics i q\u00FCestions sobre teoria d'anells. Aquesta correspond\u00E8ncia \u00E9s l'especificitat de la geometria algebraica."@ca , "Algebraick\u00E1 varieta je matematick\u00FD pojem z oboru algebraick\u00E9 geometrie. Naz\u00FDv\u00E1 se tak mno\u017Eina v\u0161ech soustavy polynomi\u00E1ln\u00EDch rovnic \u2026"@cs , "( \uC774 \uBB38\uC11C\uB294 \uB300\uC218\uAE30\uD558\uD559\uC5D0\uC11C \uBC29\uC815\uC2DD\uC758 \uD574\uC758 \uC9D1\uD569\uC5D0 \uAD00\uD55C \uAC83\uC785\uB2C8\uB2E4. \uC77C\uB828\uC758 \uD56D\uB4F1\uC2DD\uB4E4\uC744 \uB9CC\uC871\uC2DC\uD0A4\uB294 \uB300\uC218 \uAD6C\uC870\uB4E4\uC758 \uBAA8\uC784\uC5D0 \uB300\uD574\uC11C\uB294 \uB300\uC218 \uAD6C\uC870 \uB2E4\uC591\uCCB4 \uBB38\uC11C\uB97C \uCC38\uACE0\uD558\uC2ED\uC2DC\uC624.) \uB300\uC218\uAE30\uD558\uD559\uC5D0\uC11C \uB300\uC218\uB2E4\uC591\uCCB4(\u4EE3\u6578\u591A\u6A23\u9AD4, \uC601\uC5B4: algebraic variety)\uB294 \uAD6D\uC18C\uC801\uC73C\uB85C \uB2E4\uD56D\uC2DD\uB4E4\uB85C \uC8FC\uC5B4\uC9C0\uB294 \uBC29\uC815\uC2DD\uB4E4\uC758 \uC601\uC810 \uC9D1\uD569\uCC98\uB7FC \uBCF4\uC774\uB294 \uACF5\uAC04\uC774\uB2E4. \uACE0\uC804\uC801 \uB300\uC218\uAE30\uD558\uD559\uC5D0\uC11C \uB2E4\uB8E8\uB294 \uAE30\uBCF8\uC801\uC778 \uB300\uC0C1\uC774\uB2E4."@ko . @prefix gold: . dbr:Algebraic_variety gold:hypernym dbr:Objects . @prefix prov: . dbr:Algebraic_variety prov:wasDerivedFrom . @prefix xsd: . dbr:Algebraic_variety dbo:wikiPageLength "39793"^^xsd:nonNegativeInteger . @prefix wikipedia-en: . dbr:Algebraic_variety foaf:isPrimaryTopicOf wikipedia-en:Algebraic_variety .