. "Un morphisme d'anneaux est une application entre deux anneaux (unitaires) A et B, compatible avec les lois de ces anneaux et qui envoie le neutre multiplicatif de A sur le neutre multiplicatif de B."@fr . "1113808722"^^ . . . . "Omomorfismo di anelli"@it . "\u0413\u043E\u043C\u043E\u043C\u043E\u0440\u0444\u0456\u0437\u043C\u043E\u043C \u043A\u0456\u043B\u0435\u0446\u044C \u043D\u0430\u0437\u0438\u0432\u0430\u0454\u0442\u044C\u0441\u044F \u0434\u0435\u044F\u043A\u0435 \u0432\u0456\u0434\u043E\u0431\u0440\u0430\u0436\u0435\u043D\u043D\u044F \u043E\u0434\u043D\u043E\u0433\u043E \u043A\u0456\u043B\u044C\u0446\u044F \u0432 \u0456\u043D\u0448\u0435, \u0449\u043E \u0443\u0437\u0433\u043E\u0434\u0436\u0443\u0454\u0442\u044C\u0441\u044F \u0437 \u043E\u043F\u0435\u0440\u0430\u0446\u0456\u044F\u043C\u0438 \u0434\u043E\u0434\u0430\u0432\u0430\u043D\u043D\u044F \u0456 \u043C\u043D\u043E\u0436\u0435\u043D\u043D\u044F."@uk . . "26411"^^ . . . . . . . . "\u0388\u03C3\u03C4\u03C9 \u03BA\u03B1\u03B9 \u03B4\u03CD\u03BF \u03B4\u03B1\u03BA\u03C4\u03CD\u03BB\u03B9\u03BF\u03B9. \u039C\u03AF\u03B1 \u03B1\u03C0\u03B5\u03B9\u03BA\u03CC\u03BD\u03B9\u03C3\u03B7 \u03BF\u03BD\u03BF\u03BC\u03AC\u03B6\u03B5\u03C4\u03B1\u03B9 \u03BF\u03BC\u03BF\u03BC\u03BF\u03C1\u03C6\u03B9\u03C3\u03BC\u03CC\u03C2 \u03B4\u03B1\u03BA\u03C4\u03C5\u03BB\u03AF\u03C9\u03BD \u03B1\u03BD \u03B9\u03C3\u03C7\u03CD\u03BF\u03C5\u03BD \u03C4\u03B1 \u03B5\u03BE\u03AE\u03C2: \u03B3\u03B9\u03B1 \u03BA\u03AC\u03B8\u03B5 . \u0391\u03BD \u03B5\u03C0\u03B9\u03C0\u03BB\u03AD\u03BF\u03BD \u03B7 \u03C6 \u03B5\u03AF\u03BD\u03B1\u03B9 1-1 \u03B8\u03B1 \u03BF\u03BD\u03BF\u03BC\u03AC\u03B6\u03B5\u03C4\u03B1\u03B9 \u03BC\u03BF\u03BD\u03BF\u03BC\u03BF\u03C1\u03C6\u03B9\u03C3\u03BC\u03CC\u03C2 \u03B4\u03B1\u03BA\u03C4\u03C5\u03BB\u03AF\u03C9\u03BD, \u03B5\u03BD\u03CE \u03B1\u03BD \u03B5\u03AF\u03BD\u03B1\u03B9 \u03B5\u03C0\u03AF \u03B8\u03B1 \u03BF\u03BD\u03BF\u03BC\u03AC\u03B6\u03B5\u03C4\u03B1\u03B9 \u03B5\u03C0\u03B9\u03BC\u03BF\u03C1\u03C6\u03B9\u03C3\u03BC\u03CC\u03C2 \u03B4\u03B1\u03BA\u03C4\u03C5\u03BB\u03AF\u03C9\u03BD. \u0391\u03BD \u03C4\u03C5\u03C7\u03B1\u03AF\u03BD\u03B5\u03B9 \u03B7 \u03C6 \u03BD\u03B1 \u03B5\u03AF\u03BD\u03B1\u03B9 1-1 \u03BA\u03B1\u03B9 \u03B5\u03C0\u03AF \u03C4\u03CC\u03C4\u03B5 \u03BF\u03BD\u03BF\u03BC\u03AC\u03B6\u03B5\u03C4\u03B1\u03B9 \u03B9\u03C3\u03BF\u03BC\u03BF\u03C1\u03C6\u03B9\u03C3\u03BC\u03CC\u03C2 \u03B4\u03B1\u03BA\u03C4\u03C5\u03BB\u03AF\u03C9\u03BD."@el . . "Homomorfizm pier\u015Bcieni \u2013 przekszta\u0142cenie z jednego pier\u015Bcienia w drugi zachowuj\u0105ce struktur\u0119."@pl . "In der Ringtheorie betrachtet man spezielle Abbildungen zwischen Ringen, die man Ringhomomorphismen nennt. Ein Ringhomomorphismus ist eine strukturerhaltende Abbildung zwischen Ringen, und damit ein spezieller Homomorphismus."@de . . . "In de ringtheorie, een deelgebied van de abstracte algebra, een deelgebied van de wiskunde, is een ringhomomorfisme een functie tussen twee ringen die de operaties van optellen en vermenigvuldigen respecteert."@nl . . . "\u74B0\u8AD6\u3084\u62BD\u8C61\u4EE3\u6570\u5B66\u306B\u304A\u3044\u3066\u3001\u74B0\u6E96\u540C\u578B\uFF08\u82F1: ring homomorphism\uFF09\u306F2\u3064\u306E\u74B0\u306E\u9593\u306E\u69CB\u9020\u3092\u4FDD\u3064\u95A2\u6570\u3067\u3042\u308B\u3002 \u304D\u3061\u3093\u3068\u66F8\u304F\u3068\u3001R \u3068 S \u304C\u74B0\u3067\u3042\u308C\u3070\u3001\u74B0\u6E96\u540C\u578B\u306F\u4EE5\u4E0B\u3092\u6E80\u305F\u3059\u95A2\u6570 f : R \u2192 S \u3067\u3042\u308B\u3002 \n* R \u306E\u3059\u3079\u3066\u306E\u5143 a \u3068 b \u306B\u5BFE\u3057\u3066\u3001f(a + b) = f(a) + f(b) \n* R \u306E\u3059\u3079\u3066\u306E\u5143 a \u3068 b \u306B\u5BFE\u3057\u3066\u3001f(ab) = f(a) f(b) \n* f(1R) = 1S \uFF08\u52A0\u6CD5\u306E\u9006\u5143\u3068\u52A0\u6CD5\u306E\u5358\u4F4D\u5143\u3082\u69CB\u9020\u306E\u4E00\u90E8\u3067\u3042\u308B\u304C\u3001\u305D\u308C\u3089\u3092\u660E\u793A\u7684\u306B\u8981\u6C42\u3059\u308B\u5FC5\u8981\u306F\u306A\u3044\u3002\u3068\u3044\u3046\u306E\u3082\u305D\u306E\u6761\u4EF6\u306F\u4E0A\u8A18\u306E\u6761\u4EF6\u304B\u3089\u5F93\u3046\u304B\u3089\u3067\u3042\u308B\u3002\u4E00\u65B9\u3001\u6761\u4EF6 f(1R) = 1S \u3092\u843D\u3068\u3059\u3068\u4E0B\u8A18\u306E\u6027\u8CEA\u306E\u3044\u304F\u3064\u304B\u306F\u6210\u308A\u7ACB\u305F\u306A\u304F\u306A\u308B\u3002 \u3000\u8FFD\u8A18\uFF1A\u300C\u6761\u4EF6 f(1R) = 1S \u3092\u843D\u3068\u3059\u3068\u4E0B\u8A18\u306E\u6027\u8CEA\u306E\u3044\u304F\u3064\u304B\u306F\u6210\u308A\u7ACB\u305F\u306A\u304F\u306A\u308B\u300D\u3068\u3042\u308B\u304C\u3001\u74B0\u6E96\u540C\u578B\u306F\u4E57\u6CD5\u306B\u304A\u3044\u3066\u7FA4\u6E96\u540C\u578B\u3067\u3082\u3042\u308B\u305F\u3081\u3001\u7FA4\u6E96\u540C\u578B\u306E\u6027\u8CEA\u304B\u3089\u540C\u69D8\u306B\u3057\u3066\u74B0\u6E96\u540C\u578B\u306F\u52A0\u6CD5\u30FB\u4E57\u6CD5\u4E21\u65B9\u306B\u304A\u3044\u3066\u3092\u306B\u5BFE\u5FDC\u3055\u305B\u308B\u3002\u6761\u4EF6\u304B\u3089\u7701\u3044\u305F\u3068\u3057\u3066\u3082f(ab) = f(a) f(b)\u3088\u308A b \u306B 1R \u3092\u4EE3\u5165\u3059\u308B\u3053\u3068\u306B\u3088\u308A\u5358\u4F4D\u5143\u306E\u5B9A\u7FA9\u304B\u3089 f(1R) = 1S. \u3092\u5C0E\u51FA\u3059\u308B\u3053\u3068\u304C\u3067\u304D\u308B\u3002\u52A0\u6CD5\u306B\u304A\u3051\u308B\u5358\u4F4D\u5143\u3082\u540C\u69D8\u306B\u3057\u3066\u52A0\u6CD5\u306B\u304A\u3051\u308B\u7FA4\u6E96\u540C\u6027\u304B\u3089f(a + b) = f(a) + f(b) \u306B\u540C\u3058\u3088\u3046\u306B\u4EE3\u5165\u3057\u3066\u6C42\u3081\u3089\u308C\u308B\u3002\uFF09"@ja . . "Homomorfismo de an\u00E9is"@pt . "In de ringtheorie, een deelgebied van de abstracte algebra, een deelgebied van de wiskunde, is een ringhomomorfisme een functie tussen twee ringen die de operaties van optellen en vermenigvuldigen respecteert."@nl . . . . "Okruhov\u00FD homomorfismus"@cs . "Un morphisme d'anneaux est une application entre deux anneaux (unitaires) A et B, compatible avec les lois de ces anneaux et qui envoie le neutre multiplicatif de A sur le neutre multiplicatif de B."@fr . "In algebra, un omomorfismo di anelli \u00E8 una funzione fra due anelli che conserva le due operazioni di addizione e moltiplicazione."@it . "En ringo-teorio, ringa homomorfio estas funkcio inter du ringoj konservanta la algebran strukturon (adicion kaj multiplikon) de la ringoj."@eo . . "Ring homomorphism"@en . "En ringo-teorio, ringa homomorfio estas funkcio inter du ringoj konservanta la algebran strukturon (adicion kaj multiplikon) de la ringoj."@eo . . "In der Ringtheorie betrachtet man spezielle Abbildungen zwischen Ringen, die man Ringhomomorphismen nennt. Ein Ringhomomorphismus ist eine strukturerhaltende Abbildung zwischen Ringen, und damit ein spezieller Homomorphismus."@de . . . "Em \u00E1lgebra abstrata um homomorfismo de an\u00E9is \u00E9 uma fun\u00E7\u00E3o entre dois an\u00E9is que, de certa forma, preserva as opera\u00E7\u00F5es bin\u00E1rias de adi\u00E7\u00E3o e multiplica\u00E7\u00E3o. Em termos mais precisos, se e s\u00E3o an\u00E9is ent\u00E3o a fun\u00E7\u00E3o \u00E9 um homomorfismo de an\u00E9is se: \n* \n* Se os an\u00E9is t\u00EAm identidades multiplicativas , ou seja, se s\u00E3o an\u00E9is com unidade a seguinte condi\u00E7\u00E3o costuma ser exigida: \n*"@pt . . "\u039F\u03BC\u03BF\u03BC\u03BF\u03C1\u03C6\u03B9\u03C3\u03BC\u03CC\u03C2 \u03B4\u03B1\u03BA\u03C4\u03C5\u03BB\u03AF\u03C9\u03BD"@el . . . . . . . "12769"^^ . . "In algebra, un omomorfismo di anelli \u00E8 una funzione fra due anelli che conserva le due operazioni di addizione e moltiplicazione."@it . . . "\u0413\u043E\u043C\u043E\u043C\u043E\u0440\u0444\u0456\u0437\u043C\u043E\u043C \u043A\u0456\u043B\u0435\u0446\u044C \u043D\u0430\u0437\u0438\u0432\u0430\u0454\u0442\u044C\u0441\u044F \u0434\u0435\u044F\u043A\u0435 \u0432\u0456\u0434\u043E\u0431\u0440\u0430\u0436\u0435\u043D\u043D\u044F \u043E\u0434\u043D\u043E\u0433\u043E \u043A\u0456\u043B\u044C\u0446\u044F \u0432 \u0456\u043D\u0448\u0435, \u0449\u043E \u0443\u0437\u0433\u043E\u0434\u0436\u0443\u0454\u0442\u044C\u0441\u044F \u0437 \u043E\u043F\u0435\u0440\u0430\u0446\u0456\u044F\u043C\u0438 \u0434\u043E\u0434\u0430\u0432\u0430\u043D\u043D\u044F \u0456 \u043C\u043D\u043E\u0436\u0435\u043D\u043D\u044F."@uk . "Ringhomomorphismus"@de . . . . "Em \u00E1lgebra abstrata um homomorfismo de an\u00E9is \u00E9 uma fun\u00E7\u00E3o entre dois an\u00E9is que, de certa forma, preserva as opera\u00E7\u00F5es bin\u00E1rias de adi\u00E7\u00E3o e multiplica\u00E7\u00E3o. Em termos mais precisos, se e s\u00E3o an\u00E9is ent\u00E3o a fun\u00E7\u00E3o \u00E9 um homomorfismo de an\u00E9is se: \n* \n* Se os an\u00E9is t\u00EAm identidades multiplicativas , ou seja, se s\u00E3o an\u00E9is com unidade a seguinte condi\u00E7\u00E3o costuma ser exigida: \n*"@pt . . "\uD658 \uC900\uB3D9\uD615\uC0AC\uC0C1"@ko . . . "\u0413\u043E\u043C\u043E\u043C\u043E\u0440\u0444\u0456\u0437\u043C \u043A\u0456\u043B\u0435\u0446\u044C"@uk . . . . "Homomorfismo de anillos"@es . "\u74B0\u8AD6\u3084\u62BD\u8C61\u4EE3\u6570\u5B66\u306B\u304A\u3044\u3066\u3001\u74B0\u6E96\u540C\u578B\uFF08\u82F1: ring homomorphism\uFF09\u306F2\u3064\u306E\u74B0\u306E\u9593\u306E\u69CB\u9020\u3092\u4FDD\u3064\u95A2\u6570\u3067\u3042\u308B\u3002 \u304D\u3061\u3093\u3068\u66F8\u304F\u3068\u3001R \u3068 S \u304C\u74B0\u3067\u3042\u308C\u3070\u3001\u74B0\u6E96\u540C\u578B\u306F\u4EE5\u4E0B\u3092\u6E80\u305F\u3059\u95A2\u6570 f : R \u2192 S \u3067\u3042\u308B\u3002 \n* R \u306E\u3059\u3079\u3066\u306E\u5143 a \u3068 b \u306B\u5BFE\u3057\u3066\u3001f(a + b) = f(a) + f(b) \n* R \u306E\u3059\u3079\u3066\u306E\u5143 a \u3068 b \u306B\u5BFE\u3057\u3066\u3001f(ab) = f(a) f(b) \n* f(1R) = 1S \uFF08\u52A0\u6CD5\u306E\u9006\u5143\u3068\u52A0\u6CD5\u306E\u5358\u4F4D\u5143\u3082\u69CB\u9020\u306E\u4E00\u90E8\u3067\u3042\u308B\u304C\u3001\u305D\u308C\u3089\u3092\u660E\u793A\u7684\u306B\u8981\u6C42\u3059\u308B\u5FC5\u8981\u306F\u306A\u3044\u3002\u3068\u3044\u3046\u306E\u3082\u305D\u306E\u6761\u4EF6\u306F\u4E0A\u8A18\u306E\u6761\u4EF6\u304B\u3089\u5F93\u3046\u304B\u3089\u3067\u3042\u308B\u3002\u4E00\u65B9\u3001\u6761\u4EF6 f(1R) = 1S \u3092\u843D\u3068\u3059\u3068\u4E0B\u8A18\u306E\u6027\u8CEA\u306E\u3044\u304F\u3064\u304B\u306F\u6210\u308A\u7ACB\u305F\u306A\u304F\u306A\u308B\u3002 \u3000\u8FFD\u8A18\uFF1A\u300C\u6761\u4EF6 f(1R) = 1S \u3092\u843D\u3068\u3059\u3068\u4E0B\u8A18\u306E\u6027\u8CEA\u306E\u3044\u304F\u3064\u304B\u306F\u6210\u308A\u7ACB\u305F\u306A\u304F\u306A\u308B\u300D\u3068\u3042\u308B\u304C\u3001\u74B0\u6E96\u540C\u578B\u306F\u4E57\u6CD5\u306B\u304A\u3044\u3066\u7FA4\u6E96\u540C\u578B\u3067\u3082\u3042\u308B\u305F\u3081\u3001\u7FA4\u6E96\u540C\u578B\u306E\u6027\u8CEA\u304B\u3089\u540C\u69D8\u306B\u3057\u3066\u74B0\u6E96\u540C\u578B\u306F\u52A0\u6CD5\u30FB\u4E57\u6CD5\u4E21\u65B9\u306B\u304A\u3044\u3066\u3092\u306B\u5BFE\u5FDC\u3055\u305B\u308B\u3002\u6761\u4EF6\u304B\u3089\u7701\u3044\u305F\u3068\u3057\u3066\u3082f(ab) = f(a) f(b)\u3088\u308A b \u306B 1R \u3092\u4EE3\u5165\u3059\u308B\u3053\u3068\u306B\u3088\u308A\u5358\u4F4D\u5143\u306E\u5B9A\u7FA9\u304B\u3089 f(1R) = 1S. \u3092\u5C0E\u51FA\u3059\u308B\u3053\u3068\u304C\u3067\u304D\u308B\u3002\u52A0\u6CD5\u306B\u304A\u3051\u308B\u5358\u4F4D\u5143\u3082\u540C\u69D8\u306B\u3057\u3066\u52A0\u6CD5\u306B\u304A\u3051\u308B\u7FA4\u6E96\u540C\u6027\u304B\u3089f(a + b) = f(a) + f(b) \u306B\u540C\u3058\u3088\u3046\u306B\u4EE3\u5165\u3057\u3066\u6C42\u3081\u3089\u308C\u308B\u3002\uFF09 R \u3068 S \u304Crng\uFF08\u64EC\u74B0\u3084\u975E\u5358\u4F4D\u7684\u74B0\u3068\u3082\u3044\u3046\uFF09\u3067\u3042\u308C\u3070\u3001\u81EA\u7136\u306A\u6982\u5FF5\u306Frng \u6E96\u540C\u578B\u3067\u3042\u308A\u3001\u3053\u308C\u306F\u4E0A\u8A18\u304B\u30893\u3064\u76EE\u306E\u6761\u4EF6 f(1R) = 1S \u3092\u9664\u3044\u305F\u3082\u306E\u3068\u3057\u3066\u5B9A\u7FA9\u3055\u308C\u308B\u3002\uFF08\u5358\u4F4D\u7684\uFF09\u74B0\u306E\u9593\u306E\u74B0\u6E96\u540C\u578B\u3067\u306A\u3044 rng \u6E96\u540C\u578B\u3092\u8003\u3048\u308B\u3053\u3068\u304C\u3067\u304D\u308B\u3002 2\u3064\u306E\u74B0\u6E96\u540C\u578B\u306E\u5408\u6210\u306F\u74B0\u6E96\u540C\u578B\u3067\u3042\u308B\u3002\u3053\u308C\u306B\u3088\u3063\u3066\u3059\u3079\u3066\u306E\u74B0\u304B\u3089\u306A\u308B\u30AF\u30E9\u30B9\u306F\u5C04\u3092\u74B0\u6E96\u540C\u578B\u3068\u3057\u3066\u570F\u3092\u306A\u3059\uFF08cf. \u74B0\u306E\u570F\uFF09\u3002\u3068\u304F\u306B\u3001\u74B0\u81EA\u5DF1\u6E96\u540C\u578B\u3001\u74B0\u540C\u578B\u3001\u74B0\u81EA\u5DF1\u540C\u578B\u306E\u6982\u5FF5\u3092\u5F97\u308B\u3002"@ja . . . "\u73AF\u540C\u6001"@zh . "\u74B0\u6E96\u540C\u578B"@ja . . . . . . . . "Homomorfizm pier\u015Bcieni \u2013 przekszta\u0142cenie z jednego pier\u015Bcienia w drugi zachowuj\u0105ce struktur\u0119."@pl . . . . . . . . "\u5728\u73AF\u8BBA\u6216\u62BD\u8C61\u4EE3\u6570\u4E2D\uFF0C\u73AF\u540C\u6001\u662F\u6307\u4E24\u4E2A\u73AFR\u8207S\u4E4B\u95F4\u7684\u6620\u5C04f\u4FDD\u6301\u4E24\u4E2A\u73AF\u7684\u52A0\u6CD5\u4E0E\u4E58\u6CD5\u8FD0\u7B97\u3002 \u66F4\u52A0\u7CBE\u786E\u5730\uFF0C\u5982\u679CR\u548CS\u662F\u73AF\uFF0C\u5219\u73AF\u540C\u6001\u662F\u4E00\u4E2A\u51FD\u6570f : R \u2192 S\uFF0C\u4F7F\u5F97\uFF1A \n* f(a + b) = f(a) + f(b)\uFF0C\u5BF9\u4E8ER\u5185\u7684\u6240\u6709a\u548Cb\uFF1B \n* f(ab) = f(a) f(b)\uFF0C\u5BF9\u4E8ER\u5185\u7684\u6240\u6709a\u548Cb\uFF1B \n* f(1) = 1\u3002 \u5982\u679C\u6211\u4EEC\u4E0D\u8981\u6C42\u73AF\u5177\u6709\u4E58\u6CD5\u5355\u4F4D\u5143\uFF0C\u5219\u6700\u540E\u4E00\u4E2A\u6761\u4EF6\u4E0D\u9700\u8981\u3002"@zh . "Ringa homomorfio"@eo . . . "\u0388\u03C3\u03C4\u03C9 \u03BA\u03B1\u03B9 \u03B4\u03CD\u03BF \u03B4\u03B1\u03BA\u03C4\u03CD\u03BB\u03B9\u03BF\u03B9. \u039C\u03AF\u03B1 \u03B1\u03C0\u03B5\u03B9\u03BA\u03CC\u03BD\u03B9\u03C3\u03B7 \u03BF\u03BD\u03BF\u03BC\u03AC\u03B6\u03B5\u03C4\u03B1\u03B9 \u03BF\u03BC\u03BF\u03BC\u03BF\u03C1\u03C6\u03B9\u03C3\u03BC\u03CC\u03C2 \u03B4\u03B1\u03BA\u03C4\u03C5\u03BB\u03AF\u03C9\u03BD \u03B1\u03BD \u03B9\u03C3\u03C7\u03CD\u03BF\u03C5\u03BD \u03C4\u03B1 \u03B5\u03BE\u03AE\u03C2: \u03B3\u03B9\u03B1 \u03BA\u03AC\u03B8\u03B5 . \u0391\u03BD \u03B5\u03C0\u03B9\u03C0\u03BB\u03AD\u03BF\u03BD \u03B7 \u03C6 \u03B5\u03AF\u03BD\u03B1\u03B9 1-1 \u03B8\u03B1 \u03BF\u03BD\u03BF\u03BC\u03AC\u03B6\u03B5\u03C4\u03B1\u03B9 \u03BC\u03BF\u03BD\u03BF\u03BC\u03BF\u03C1\u03C6\u03B9\u03C3\u03BC\u03CC\u03C2 \u03B4\u03B1\u03BA\u03C4\u03C5\u03BB\u03AF\u03C9\u03BD, \u03B5\u03BD\u03CE \u03B1\u03BD \u03B5\u03AF\u03BD\u03B1\u03B9 \u03B5\u03C0\u03AF \u03B8\u03B1 \u03BF\u03BD\u03BF\u03BC\u03AC\u03B6\u03B5\u03C4\u03B1\u03B9 \u03B5\u03C0\u03B9\u03BC\u03BF\u03C1\u03C6\u03B9\u03C3\u03BC\u03CC\u03C2 \u03B4\u03B1\u03BA\u03C4\u03C5\u03BB\u03AF\u03C9\u03BD. \u0391\u03BD \u03C4\u03C5\u03C7\u03B1\u03AF\u03BD\u03B5\u03B9 \u03B7 \u03C6 \u03BD\u03B1 \u03B5\u03AF\u03BD\u03B1\u03B9 1-1 \u03BA\u03B1\u03B9 \u03B5\u03C0\u03AF \u03C4\u03CC\u03C4\u03B5 \u03BF\u03BD\u03BF\u03BC\u03AC\u03B6\u03B5\u03C4\u03B1\u03B9 \u03B9\u03C3\u03BF\u03BC\u03BF\u03C1\u03C6\u03B9\u03C3\u03BC\u03CC\u03C2 \u03B4\u03B1\u03BA\u03C4\u03C5\u03BB\u03AF\u03C9\u03BD. \u03A0\u03B1\u03C1\u03B1\u03C4\u03B7\u03C1\u03BF\u03CD\u03BC\u03B5 \u03B4\u03B7\u03BB\u03B1\u03B4\u03AE \u03CC\u03C4\u03B9 \u03BF\u03B9 \u03BF\u03BC\u03BF\u03BC\u03BF\u03C1\u03C6\u03B9\u03C3\u03BC\u03BF\u03AF \u03B4\u03B1\u03BA\u03C4\u03C5\u03BB\u03AF\u03C9\u03BD \u00AB\u03B4\u03B9\u03B1\u03C4\u03B7\u03C1\u03BF\u03CD\u03BD\u00BB \u03C4\u03B9\u03C2 \u03C0\u03C1\u03AC\u03BE\u03B5\u03B9\u03C2, \u03BA\u03AC\u03C4\u03B9 \u03C4\u03BF \u03BF\u03C0\u03BF\u03AF\u03BF \u03C3\u03C5\u03BC\u03B2\u03B1\u03AF\u03BD\u03B5\u03B9 \u03BA\u03B1\u03B9 \u03BC\u03B5 \u03C4\u03B9\u03C2 \u03B3\u03C1\u03B1\u03BC\u03BC\u03B9\u03BA\u03AD\u03C2 \u03B1\u03C0\u03B5\u03B9\u03BA\u03BF\u03BD\u03AF\u03C3\u03B5\u03B9\u03C2 \u03BC\u03B5\u03C4\u03B1\u03BE\u03CD \u03B4\u03B9\u03B1\u03BD\u03C5\u03C3\u03BC\u03B1\u03C4\u03B9\u03BA\u03CE\u03BD \u03C7\u03CE\u03C1\u03C9\u03BD. \u0395\u03C0\u03AF\u03C3\u03B7\u03C2 \u03B1\u03C5\u03C4\u03BF\u03AF \u03B5\u03AF\u03BD\u03B1\u03B9 \u03C4\u03BF \u03BC\u03AD\u03C3\u03BF \u03B5\u03BA\u03B5\u03AF\u03BD\u03BF \u03C0\u03BF\u03C5 \u03B8\u03B1 \u03BC\u03B1\u03C2 \u03B5\u03C0\u03B9\u03C4\u03C1\u03AD\u03C8\u03B5\u03B9 \u03BD\u03B1 \u03C4\u03BF\u03C5\u03C2 \u03B4\u03B9\u03B1\u03C6\u03CC\u03C1\u03BF\u03C5\u03C2 \u03B4\u03B1\u03BA\u03C4\u03C5\u03BB\u03AF\u03BF\u03C5\u03C2, \u03CC\u03C0\u03BF\u03C5 \u03BC\u03B5 \u03C4\u03BF\u03BD \u03CC\u03C1\u03BF \"\u03C4\u03B1\u03BE\u03B9\u03BD\u03CC\u03BC\u03B7\u03C3\u03B7\" \u03B5\u03BD\u03BD\u03BF\u03BF\u03CD\u03BC\u03B5 \u03C4\u03B7\u03BD \u03C4\u03B1\u03C5\u03C4\u03BF\u03C0\u03BF\u03AF\u03B7\u03C3\u03B7 \u03C4\u03C9\u03BD \u03BC\u03B5\u03BB\u03CE\u03BD \u03BC\u03B9\u03B1\u03C2 \u03B8\u03B5\u03C9\u03C1\u03AF\u03B1\u03C2 \u03B7 \u03BF\u03C0\u03BF\u03AF\u03B1 \u03B5\u03AF\u03BD\u03B1\u03B9 \u03B5\u03C5\u03C1\u03CD\u03C4\u03B5\u03C1\u03B7 \u03C4\u03B7\u03C2 \u03B9\u03C3\u03CC\u03C4\u03B7\u03C4\u03B1\u03C2. \u0395\u03B9\u03B4\u03B9\u03BA\u03CC\u03C4\u03B5\u03C1\u03B1 \u03BF\u03B9 \u03B9\u03C3\u03BF\u03BC\u03BF\u03C1\u03C6\u03B9\u03C3\u03BC\u03BF\u03AF, \u03CC\u03C0\u03C9\u03C2 \u03BF\u03C1\u03AF\u03C3\u03C4\u03B7\u03BA\u03B1\u03BD \u03C0\u03B1\u03C1\u03B1\u03C0\u03AC\u03BD\u03C9, \u03B5\u03AF\u03BD\u03B1\u03B9 \u03AD\u03BD\u03B1 \u03BC\u03AD\u03C3\u03BF \u03BC\u03B5 \u03C4\u03BF \u03BF\u03C0\u03BF\u03AF\u03BF \u03BC\u03C0\u03BF\u03C1\u03BF\u03CD\u03BC\u03B5 \u03BD\u03B1 \u03C4\u03B1\u03C5\u03C4\u03AF\u03B6\u03BF\u03C5\u03BC\u03B5 \u03B4\u03C5\u03BF \u03B4\u03B1\u03BA\u03C4\u03C5\u03BB\u03AF\u03BF\u03C5\u03C2."@el . . . . . . . "In ring theory, a branch of abstract algebra, a ring homomorphism is a structure-preserving function between two rings. More explicitly, if R and S are rings, then a ring homomorphism is a function f : R \u2192 S such that f is: addition preserving: for all a and b in R,multiplication preserving: for all a and b in R,and unit (multiplicative identity) preserving:. Additive inverses and the additive identity are part of the structure too, but it is not necessary to require explicitly that they too are respected, because these conditions are consequences of the three conditions above."@en . . . "V teorii okruh\u016F \u010Di obecn\u011Bji v abstraktn\u00ED algeb\u0159e se okruhov\u00FDm homomorfismem rozum\u00ED homomorfismus mezi dv\u011Bma okruhy. Je to tedy ka\u017Ed\u00E1 funkce mezi dv\u011Bma okruhy, kter\u00E1 je slu\u010Diteln\u00E1 se s\u010D\u00EDt\u00E1n\u00EDm a n\u00E1soben\u00EDm v okruz\u00EDch, neboli takov\u00E1 funkce f : R \u2192 S, kter\u00E1 spl\u0148uje: \n* f(a + b) = f(a) + f(b) pro v\u0161echna a a b z R \n* f(ab) = f(a) f(b) pro v\u0161echna a a b z R kde (R,+,\u00B7) a (S,+,\u00B7) jsou \u0159e\u010Den\u00E9 okruhy. Plat\u00ED, \u017Ee slo\u017Een\u00ED okruhov\u00FDch homomorfism\u016F je op\u011Bt okruhov\u00FD homomorfismus, z \u010Deho\u017E plyne, \u017Ee t\u0159\u00EDda v\u0161ech okruh\u016F tvo\u0159\u00ED kategorii s okruhov\u00FDmi homomorfismy coby morfismy."@cs . . "\u5728\u73AF\u8BBA\u6216\u62BD\u8C61\u4EE3\u6570\u4E2D\uFF0C\u73AF\u540C\u6001\u662F\u6307\u4E24\u4E2A\u73AFR\u8207S\u4E4B\u95F4\u7684\u6620\u5C04f\u4FDD\u6301\u4E24\u4E2A\u73AF\u7684\u52A0\u6CD5\u4E0E\u4E58\u6CD5\u8FD0\u7B97\u3002 \u66F4\u52A0\u7CBE\u786E\u5730\uFF0C\u5982\u679CR\u548CS\u662F\u73AF\uFF0C\u5219\u73AF\u540C\u6001\u662F\u4E00\u4E2A\u51FD\u6570f : R \u2192 S\uFF0C\u4F7F\u5F97\uFF1A \n* f(a + b) = f(a) + f(b)\uFF0C\u5BF9\u4E8ER\u5185\u7684\u6240\u6709a\u548Cb\uFF1B \n* f(ab) = f(a) f(b)\uFF0C\u5BF9\u4E8ER\u5185\u7684\u6240\u6709a\u548Cb\uFF1B \n* f(1) = 1\u3002 \u5982\u679C\u6211\u4EEC\u4E0D\u8981\u6C42\u73AF\u5177\u6709\u4E58\u6CD5\u5355\u4F4D\u5143\uFF0C\u5219\u6700\u540E\u4E00\u4E2A\u6761\u4EF6\u4E0D\u9700\u8981\u3002"@zh . . . . "In ring theory, a branch of abstract algebra, a ring homomorphism is a structure-preserving function between two rings. More explicitly, if R and S are rings, then a ring homomorphism is a function f : R \u2192 S such that f is: addition preserving: for all a and b in R,multiplication preserving: for all a and b in R,and unit (multiplicative identity) preserving:. Additive inverses and the additive identity are part of the structure too, but it is not necessary to require explicitly that they too are respected, because these conditions are consequences of the three conditions above. If in addition f is a bijection, then its inverse f\u22121 is also a ring homomorphism. In this case, f is called a ring isomorphism, and the rings R and S are called isomorphic. From the standpoint of ring theory, isomorphic rings cannot be distinguished. If R and S are rngs, then the corresponding notion is that of a rng homomorphism, defined as above except without the third condition f(1R) = 1S. A rng homomorphism between (unital) rings need not be a ring homomorphism. The composition of two ring homomorphisms is a ring homomorphism. It follows that the class of all rings forms a category with ring homomorphisms as the morphisms (cf. the category of rings).In particular, one obtains the notions of ring endomorphism, ring isomorphism, and ring automorphism."@en . . . . "Un homomorfismo de anillos es una aplicaci\u00F3n entre anillos que conserva las estructuras de ambos como anillos. En todo el art\u00EDculo y son anillos."@es . . . . . . . . . "Ringhomomorfisme"@nl . . . "Homomorfizm pier\u015Bcieni"@pl . . "Un homomorfismo de anillos es una aplicaci\u00F3n entre anillos que conserva las estructuras de ambos como anillos. En todo el art\u00EDculo y son anillos."@es . . "Morphisme d'anneaux"@fr . "V teorii okruh\u016F \u010Di obecn\u011Bji v abstraktn\u00ED algeb\u0159e se okruhov\u00FDm homomorfismem rozum\u00ED homomorfismus mezi dv\u011Bma okruhy. Je to tedy ka\u017Ed\u00E1 funkce mezi dv\u011Bma okruhy, kter\u00E1 je slu\u010Diteln\u00E1 se s\u010D\u00EDt\u00E1n\u00EDm a n\u00E1soben\u00EDm v okruz\u00EDch, neboli takov\u00E1 funkce f : R \u2192 S, kter\u00E1 spl\u0148uje: \n* f(a + b) = f(a) + f(b) pro v\u0161echna a a b z R \n* f(ab) = f(a) f(b) pro v\u0161echna a a b z R kde (R,+,\u00B7) a (S,+,\u00B7) jsou \u0159e\u010Den\u00E9 okruhy. Plat\u00ED, \u017Ee slo\u017Een\u00ED okruhov\u00FDch homomorfism\u016F je op\u011Bt okruhov\u00FD homomorfismus, z \u010Deho\u017E plyne, \u017Ee t\u0159\u00EDda v\u0161ech okruh\u016F tvo\u0159\u00ED kategorii s okruhov\u00FDmi homomorfismy coby morfismy."@cs . .