. . . . . . . . "\u0414\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0440\u043E\u0432\u0430\u043D\u0438\u0435 \u0432 \u0430\u043B\u0433\u0435\u0431\u0440\u0435 \u2014 \u043E\u043F\u0435\u0440\u0430\u0446\u0438\u044F, \u043E\u0431\u043E\u0431\u0449\u0430\u044E\u0449\u0430\u044F \u0441\u0432\u043E\u0439\u0441\u0442\u0432\u0430 \u0440\u0430\u0437\u043B\u0438\u0447\u043D\u044B\u0445 \u043A\u043B\u0430\u0441\u0441\u0438\u0447\u0435\u0441\u043A\u0438\u0445 \u043F\u0440\u043E\u0438\u0437\u0432\u043E\u0434\u043D\u044B\u0445 \u0438 \u043F\u043E\u0437\u0432\u043E\u043B\u044F\u044E\u0449\u0430\u044F \u0432\u0432\u0435\u0441\u0442\u0438 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u043E-\u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043A\u0438\u0435 \u0438\u0434\u0435\u0438 \u0432 \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u0443\u044E \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u044E. \u0418\u0437\u043D\u0430\u0447\u0430\u043B\u044C\u043D\u043E \u044D\u0442\u043E \u043F\u043E\u043D\u044F\u0442\u0438\u0435 \u0431\u044B\u043B\u043E \u0432\u0432\u0435\u0434\u0435\u043D\u043E \u0434\u043B\u044F \u0438\u0441\u0441\u043B\u0435\u0434\u043E\u0432\u0430\u043D\u0438\u044F \u0438\u043D\u0442\u0435\u0433\u0440\u0438\u0440\u0443\u0435\u043C\u043E\u0441\u0442\u0438 \u0432\u044B\u0440\u0430\u0436\u0435\u043D\u0438\u0439 \u0432 \u044D\u043B\u0435\u043C\u0435\u043D\u0442\u0430\u0440\u043D\u044B\u0445 \u0444\u0443\u043D\u043A\u0446\u0438\u044F\u0445 \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u0438\u043C\u0438 \u043C\u0435\u0442\u043E\u0434\u0430\u043C\u0438. \u041A\u043E\u043B\u044C\u0446\u043E, \u043F\u043E\u043B\u0435, \u0430\u043B\u0433\u0435\u0431\u0440\u0430, \u043E\u0441\u043D\u0430\u0449\u0451\u043D\u043D\u044B\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0440\u043E\u0432\u0430\u043D\u0438\u0435\u043C, \u043D\u0430\u0437\u044B\u0432\u0430\u044E\u0442\u0441\u044F \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u044B\u043C \u043A\u043E\u043B\u044C\u0446\u043E\u043C, \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u044B\u043C \u043F\u043E\u043B\u0435\u043C, \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u043E\u0439 \u0430\u043B\u0433\u0435\u0431\u0440\u043E\u0439, \u0441\u043E\u043E\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043D\u043D\u043E."@ru . . . . . . "\u0414\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0440\u043E\u0432\u0430\u043D\u0438\u0435 (\u0430\u043B\u0433\u0435\u0431\u0440\u0430)"@ru . . . "En alg\u00E8bre, le terme d\u00E9rivation est employ\u00E9 dans divers contextes pour d\u00E9signer une application v\u00E9rifiant l'identit\u00E9 de Leibniz. Selon le contexte, il peut s'agir, entre autres, d'une application additive d\u00E9finie sur un anneau A \u00E0 valeurs dans un -module, ou bien d'un endomorphisme d'une alg\u00E8bre unitaire sur un anneau unitaire. Cette notion est en particulier v\u00E9rifi\u00E9e par l'op\u00E9rateur de d\u00E9rivation d'une fonction (de variable r\u00E9elle, par exemple); elle en est une g\u00E9n\u00E9ralisation utilis\u00E9e en g\u00E9om\u00E9trie alg\u00E9brique et en calcul diff\u00E9rentiel sur les vari\u00E9t\u00E9s (par exemple pour d\u00E9finir le crochet de Lie). Toute application de d\u00E9rivation v\u00E9rifie la formule de Leibniz : \n* Portail de l\u2019alg\u00E8bre"@fr . . "( \uC774 \uBB38\uC11C\uB294 \uC5B4\uB5A4 \uC774\uD56D \uC5F0\uC0B0\uC5D0 \uB300\uD558\uC5EC \uACF1 \uADDC\uCE59\uC744 \uB530\uB974\uB294 \uC120\uD615 \uBCC0\uD658\uC73C\uB85C \uAD6C\uC131\uB41C \uB9AC \uB300\uC218\uC5D0 \uAD00\uD55C \uAC83\uC785\uB2C8\uB2E4. \uC0AC\uC2AC \uBCF5\uD569\uCCB4 \uAD6C\uC870\uB97C \uAC16\uB294 \uB9AC \uCD08\uB300\uC218\uC5D0 \uB300\uD574\uC11C\uB294 \uBBF8\uBD84 \uB4F1\uAE09 \uB9AC \uB300\uC218 \uBB38\uC11C\uB97C \uCC38\uACE0\uD558\uC2ED\uC2DC\uC624.) \uB9AC \uB300\uC218 \uC774\uB860\uC5D0\uC11C, \uBBF8\uBD84 \uB9AC \uB300\uC218(\u5FAE\u5206Lie\u4EE3\u6578, \uC601\uC5B4: derivation Lie algebra)\uB294 \uC5B4\uB5A4 \uC30D\uC120\uD615 \uC774\uD56D \uC5F0\uC0B0\uC5D0 \uB300\uD55C, \uACF1 \uADDC\uCE59\uC744 \uB530\uB974\uB294 \uBBF8\uBD84 \uC5F0\uC0B0\uB4E4\uB85C \uAD6C\uC131\uB41C \uB9AC \uB300\uC218\uC774\uB2E4.:A\u2162.117, \u00A7\u2162.10.2:383, Chapter 16:190, \u00A725 \uB300\uB7B5, \uC774 \uB300\uC218 \uAD6C\uC870\uC758 \uBB34\uD55C\uC18C \uC790\uAE30 \uB3D9\uD615\uC744 \uB098\uD0C0\uB0B8\uB2E4."@ko . "\u5BFC\u5B50\uFF08\u82F1\u8A9E\uFF1Aderivation\uFF09\u5728\u62BD\u8C61\u4EE3\u6570\u4E2D\u662F\u6307\u4EE3\u6570\u4E0A\u7684\u4E00\u4E2A\u51FD\u6570\uFF0C\u63A8\u5E7F\u4E86\u5BFC\u6570\u7B97\u5B50\u7684\u67D0\u4E9B\u7279\u5F81\u3002\u660E\u786E\u5730\uFF0C\u7ED9\u5B9A\u4E00\u4E2A\u73AF\u6216\u57DF k \u4E0A\u4E00\u4E2A\u4EE3\u6570 A\uFF0C\u4E00\u4E2A k-\u5BFC\u5B50\u662F\u4E00\u4E2A k-\u7EBF\u6027\u6620\u5C04 D: A \u2192 A\uFF0C\u6EE1\u8DB3\u83B1\u5E03\u5C3C\u5179\u6CD5\u5219\uFF1A \u66F4\u4E00\u822C\u5730\uFF0C\u4ECE A \u6620\u5230 A-\u6A21 M \u7684\u4E00\u4E2A k-\u7EBF\u6027\u6620\u5C04 D\uFF0C\u6EE1\u8DB3\u83B1\u5E03\u5C3C\u5179\u6CD5\u5219\u4E5F\u79F0\u4E3A\u4E00\u4E2A\u5BFC\u5B50\u3002A \u6240\u6709\u5230\u81EA\u8EAB\u7684 k-\u5BFC\u5B50\u96C6\u5408\u8BB0\u4E3A Derk(A)\u3002\u4ECE A \u5230 A-\u6A21 M \u7684\u6240\u6709 k-\u5BFC\u5B50\u96C6\u5408\u8BB0\u4E3A Derk(A,M)\u3002 \u5BFC\u5B50\u5728\u4E0D\u540C\u7684\u6570\u5B66\u9886\u57DF\u4EE5\u8BB8\u591A\u4E0D\u540C\u7684\u9762\u8C8C\u51FA\u73B0\u3002\u5173\u4E8E\u4E00\u4E2A\u53D8\u91CF\u7684\u504F\u5BFC\u6570\u662F Rn \u4E0A\u5B9E\u503C\u53EF\u5FAE\u51FD\u6570\u7EC4\u6210\u7684\u4EE3\u6570\u4E0A\u7684\u4E00\u4E2A R-\u5BFC\u5B50\u3002\u5173\u4E8E\u4E00\u4E2A\u5411\u91CF\u573A\u7684\u674E\u5BFC\u6570\u662F\u53EF\u5FAE\u6D41\u5F62\u4E0A\u53EF\u5FAE\u51FD\u6570\u4EE3\u6570\u4E0A\u7684 R-\u5BFC\u5B50\uFF1B\u66F4\u4E00\u822C\u5730\uFF0C\u5B83\u662F\u6D41\u5F62\u4E0A\u5F20\u91CF\u4EE3\u6570\u7684\u5BFC\u5B50\u3002\u662F\u4E00\u4E2A\u62BD\u8C61\u4EE3\u6570\u4E0A\u7684\u5BFC\u5B50\u7684\u4F8B\u5B50\u3002\u5982\u679C\u4EE3\u6570 A \uFF0C\u5219\u5173\u4E8E A \u4E2D\u4E00\u4E2A\u5143\u7D20\u7684\u4EA4\u6362\u5B50\u5B9A\u4E49\u4E86 A \u5230\u81EA\u8EAB\u7684\u7EBF\u6027\u6620\u5C04\uFF0C\u8FD9\u662F A \u7684\u4E00\u4E2A k-\u5BFC\u5B50\u3002\u4E00\u4E2A\u4EE3\u6570 A \u88C5\u5907\u4E00\u4E2A\u7279\u5B9A\u7684\u5BFC\u5B50 d \u7EC4\u6210\u4E86\u4E00\u4E2A\u5FAE\u5206\u4EE3\u6570\uFF0C\u8FD9\u81EA\u8EAB\u4FBF\u662F\u4E00\u4E9B\u7814\u7A76\u9886\u57DF\u7684\u4E00\u4E2A\u91CD\u8981\u5BF9\u8C61\uFF0C\u6BD4\u5982\u5FAE\u5206\u4F3D\u7F57\u74E6\u7406\u8BBA\u3002"@zh . . . . . . "Inom algebran, \u00E4r en derivation en typ av avbildning som abstraherar deriveringsavbilningen i analysen."@sv . . . . "\u5BFC\u5B50\uFF08\u82F1\u8A9E\uFF1Aderivation\uFF09\u5728\u62BD\u8C61\u4EE3\u6570\u4E2D\u662F\u6307\u4EE3\u6570\u4E0A\u7684\u4E00\u4E2A\u51FD\u6570\uFF0C\u63A8\u5E7F\u4E86\u5BFC\u6570\u7B97\u5B50\u7684\u67D0\u4E9B\u7279\u5F81\u3002\u660E\u786E\u5730\uFF0C\u7ED9\u5B9A\u4E00\u4E2A\u73AF\u6216\u57DF k \u4E0A\u4E00\u4E2A\u4EE3\u6570 A\uFF0C\u4E00\u4E2A k-\u5BFC\u5B50\u662F\u4E00\u4E2A k-\u7EBF\u6027\u6620\u5C04 D: A \u2192 A\uFF0C\u6EE1\u8DB3\u83B1\u5E03\u5C3C\u5179\u6CD5\u5219\uFF1A \u66F4\u4E00\u822C\u5730\uFF0C\u4ECE A \u6620\u5230 A-\u6A21 M \u7684\u4E00\u4E2A k-\u7EBF\u6027\u6620\u5C04 D\uFF0C\u6EE1\u8DB3\u83B1\u5E03\u5C3C\u5179\u6CD5\u5219\u4E5F\u79F0\u4E3A\u4E00\u4E2A\u5BFC\u5B50\u3002A \u6240\u6709\u5230\u81EA\u8EAB\u7684 k-\u5BFC\u5B50\u96C6\u5408\u8BB0\u4E3A Derk(A)\u3002\u4ECE A \u5230 A-\u6A21 M \u7684\u6240\u6709 k-\u5BFC\u5B50\u96C6\u5408\u8BB0\u4E3A Derk(A,M)\u3002 \u5BFC\u5B50\u5728\u4E0D\u540C\u7684\u6570\u5B66\u9886\u57DF\u4EE5\u8BB8\u591A\u4E0D\u540C\u7684\u9762\u8C8C\u51FA\u73B0\u3002\u5173\u4E8E\u4E00\u4E2A\u53D8\u91CF\u7684\u504F\u5BFC\u6570\u662F Rn \u4E0A\u5B9E\u503C\u53EF\u5FAE\u51FD\u6570\u7EC4\u6210\u7684\u4EE3\u6570\u4E0A\u7684\u4E00\u4E2A R-\u5BFC\u5B50\u3002\u5173\u4E8E\u4E00\u4E2A\u5411\u91CF\u573A\u7684\u674E\u5BFC\u6570\u662F\u53EF\u5FAE\u6D41\u5F62\u4E0A\u53EF\u5FAE\u51FD\u6570\u4EE3\u6570\u4E0A\u7684 R-\u5BFC\u5B50\uFF1B\u66F4\u4E00\u822C\u5730\uFF0C\u5B83\u662F\u6D41\u5F62\u4E0A\u5F20\u91CF\u4EE3\u6570\u7684\u5BFC\u5B50\u3002\u662F\u4E00\u4E2A\u62BD\u8C61\u4EE3\u6570\u4E0A\u7684\u5BFC\u5B50\u7684\u4F8B\u5B50\u3002\u5982\u679C\u4EE3\u6570 A \uFF0C\u5219\u5173\u4E8E A \u4E2D\u4E00\u4E2A\u5143\u7D20\u7684\u4EA4\u6362\u5B50\u5B9A\u4E49\u4E86 A \u5230\u81EA\u8EAB\u7684\u7EBF\u6027\u6620\u5C04\uFF0C\u8FD9\u662F A \u7684\u4E00\u4E2A k-\u5BFC\u5B50\u3002\u4E00\u4E2A\u4EE3\u6570 A \u88C5\u5907\u4E00\u4E2A\u7279\u5B9A\u7684\u5BFC\u5B50 d \u7EC4\u6210\u4E86\u4E00\u4E2A\u5FAE\u5206\u4EE3\u6570\uFF0C\u8FD9\u81EA\u8EAB\u4FBF\u662F\u4E00\u4E9B\u7814\u7A76\u9886\u57DF\u7684\u4E00\u4E2A\u91CD\u8981\u5BF9\u8C61\uFF0C\u6BD4\u5982\u5FAE\u5206\u4F3D\u7F57\u74E6\u7406\u8BBA\u3002"@zh . . . "Derivation"@sv . "Derivation (Mathematik)"@de . "In verschiedenen Teilgebieten der Mathematik, insbesondere im Bereich der abstrakten Algebra, bezeichnet man Abbildungen als Derivationen, wenn sie eine bestimmte Funktionalgleichung erf\u00FCllen. Diese Gleichung wird als Leibniz-Regel bezeichnet und erinnert an die Produktregel aus der Differentialrechnung. Tats\u00E4chlich ist der Begriff der Derivation eine Abstraktion der Ableitung in den Kontext der Algebra. Eine Algebra \u00FCber einem kommutativen Ring zusammen mit einer Derivation wird auch Differentialalgebra genannt."@de . . "897658"^^ . "Dada un \u00E1lgebra, una derivaci\u00F3n es una aplicaci\u00F3n lineal D del \u00E1lgebra en s\u00ED misma que para cualesquiera satisface la regla de Leibniz:"@es . "\u0412 \u0430\u043B\u0433\u0435\u0431\u0440\u0456 \u0434\u0438\u0444\u0435\u0440\u0435\u043D\u0446\u0456\u044E\u0432\u0430\u043D\u043D\u044F \u2014 \u043E\u043F\u0435\u0440\u0430\u0446\u0456\u044F, \u0449\u043E \u0443\u0437\u0430\u0433\u0430\u043B\u044C\u043D\u044E\u0454 \u0432\u043B\u0430\u0441\u0442\u0438\u0432\u043E\u0441\u0442\u0456 \u0440\u0456\u0437\u043D\u0438\u0445 \u043A\u043B\u0430\u0441\u0438\u0447\u043D\u0438\u0445 \u043F\u043E\u0445\u0456\u0434\u043D\u0438\u0445 \u0456 \u0434\u043E\u0437\u0432\u043E\u043B\u044F\u0454 \u0432\u0432\u0435\u0441\u0442\u0438 \u0434\u0438\u0444\u0435\u0440\u0435\u043D\u0446\u0456\u0439\u043D\u043E-\u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0447\u043D\u0456 \u0456\u0434\u0435\u0457 \u0432 \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u0457\u0447\u043D\u0443 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0456\u044E. \u0421\u043F\u0435\u0440\u0448\u0443 \u043F\u043E\u043D\u044F\u0442\u0442\u044F \u0431\u0443\u043B\u043E \u0432\u0432\u0435\u0434\u0435\u043D\u043E \u0434\u043B\u044F \u0434\u043E\u0441\u043B\u0456\u0434\u0436\u0435\u043D\u043D\u044F \u0456\u043D\u0442\u0435\u0433\u0440\u043E\u0432\u0430\u043D\u043E\u0441\u0442\u0456 \u0432 \u0435\u043B\u0435\u043C\u0435\u043D\u0442\u0430\u0440\u043D\u0438\u0445 \u0444\u0443\u043D\u043A\u0446\u0456\u044F\u0445 \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u0457\u0447\u043D\u0438\u043C\u0438 \u043C\u0435\u0442\u043E\u0434\u0430\u043C\u0438."@uk . . "\uBBF8\uBD84 \uB9AC \uB300\uC218"@ko . . . . . . . . . "Derivation (differential algebra)"@en . "\u0414\u0438\u0444\u0435\u0440\u0435\u043D\u0446\u0456\u044E\u0432\u0430\u043D\u043D\u044F (\u0430\u043B\u0433\u0435\u0431\u0440\u0430)"@uk . "\u5BFC\u5B50"@zh . . . . . "6794"^^ . . . . . . . "Dada un \u00E1lgebra, una derivaci\u00F3n es una aplicaci\u00F3n lineal D del \u00E1lgebra en s\u00ED misma que para cualesquiera satisface la regla de Leibniz:"@es . . "Inom algebran, \u00E4r en derivation en typ av avbildning som abstraherar deriveringsavbilningen i analysen."@sv . "In verschiedenen Teilgebieten der Mathematik, insbesondere im Bereich der abstrakten Algebra, bezeichnet man Abbildungen als Derivationen, wenn sie eine bestimmte Funktionalgleichung erf\u00FCllen. Diese Gleichung wird als Leibniz-Regel bezeichnet und erinnert an die Produktregel aus der Differentialrechnung. Tats\u00E4chlich ist der Begriff der Derivation eine Abstraktion der Ableitung in den Kontext der Algebra. Eine Algebra \u00FCber einem kommutativen Ring zusammen mit einer Derivation wird auch Differentialalgebra genannt."@de . . . . "In mathematics, a derivation is a function on an algebra which generalizes certain features of the derivative operator. Specifically, given an algebra A over a ring or a field K, a K-derivation is a K-linear map D : A \u2192 A that satisfies Leibniz's law: More generally, if M is an A-bimodule, a K-linear map D : A \u2192 M that satisfies the Leibniz law is also called a derivation. The collection of all K-derivations of A to itself is denoted by DerK(A). The collection of K-derivations of A into an A-module M is denoted by DerK(A, M)."@en . . . . . "\u0412 \u0430\u043B\u0433\u0435\u0431\u0440\u0456 \u0434\u0438\u0444\u0435\u0440\u0435\u043D\u0446\u0456\u044E\u0432\u0430\u043D\u043D\u044F \u2014 \u043E\u043F\u0435\u0440\u0430\u0446\u0456\u044F, \u0449\u043E \u0443\u0437\u0430\u0433\u0430\u043B\u044C\u043D\u044E\u0454 \u0432\u043B\u0430\u0441\u0442\u0438\u0432\u043E\u0441\u0442\u0456 \u0440\u0456\u0437\u043D\u0438\u0445 \u043A\u043B\u0430\u0441\u0438\u0447\u043D\u0438\u0445 \u043F\u043E\u0445\u0456\u0434\u043D\u0438\u0445 \u0456 \u0434\u043E\u0437\u0432\u043E\u043B\u044F\u0454 \u0432\u0432\u0435\u0441\u0442\u0438 \u0434\u0438\u0444\u0435\u0440\u0435\u043D\u0446\u0456\u0439\u043D\u043E-\u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0447\u043D\u0456 \u0456\u0434\u0435\u0457 \u0432 \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u0457\u0447\u043D\u0443 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0456\u044E. \u0421\u043F\u0435\u0440\u0448\u0443 \u043F\u043E\u043D\u044F\u0442\u0442\u044F \u0431\u0443\u043B\u043E \u0432\u0432\u0435\u0434\u0435\u043D\u043E \u0434\u043B\u044F \u0434\u043E\u0441\u043B\u0456\u0434\u0436\u0435\u043D\u043D\u044F \u0456\u043D\u0442\u0435\u0433\u0440\u043E\u0432\u0430\u043D\u043E\u0441\u0442\u0456 \u0432 \u0435\u043B\u0435\u043C\u0435\u043D\u0442\u0430\u0440\u043D\u0438\u0445 \u0444\u0443\u043D\u043A\u0446\u0456\u044F\u0445 \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u0457\u0447\u043D\u0438\u043C\u0438 \u043C\u0435\u0442\u043E\u0434\u0430\u043C\u0438."@uk . . "D\u00E9rivation (alg\u00E8bre)"@fr . . "\u0414\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0440\u043E\u0432\u0430\u043D\u0438\u0435 \u0432 \u0430\u043B\u0433\u0435\u0431\u0440\u0435 \u2014 \u043E\u043F\u0435\u0440\u0430\u0446\u0438\u044F, \u043E\u0431\u043E\u0431\u0449\u0430\u044E\u0449\u0430\u044F \u0441\u0432\u043E\u0439\u0441\u0442\u0432\u0430 \u0440\u0430\u0437\u043B\u0438\u0447\u043D\u044B\u0445 \u043A\u043B\u0430\u0441\u0441\u0438\u0447\u0435\u0441\u043A\u0438\u0445 \u043F\u0440\u043E\u0438\u0437\u0432\u043E\u0434\u043D\u044B\u0445 \u0438 \u043F\u043E\u0437\u0432\u043E\u043B\u044F\u044E\u0449\u0430\u044F \u0432\u0432\u0435\u0441\u0442\u0438 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u043E-\u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043A\u0438\u0435 \u0438\u0434\u0435\u0438 \u0432 \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u0443\u044E \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u044E. \u0418\u0437\u043D\u0430\u0447\u0430\u043B\u044C\u043D\u043E \u044D\u0442\u043E \u043F\u043E\u043D\u044F\u0442\u0438\u0435 \u0431\u044B\u043B\u043E \u0432\u0432\u0435\u0434\u0435\u043D\u043E \u0434\u043B\u044F \u0438\u0441\u0441\u043B\u0435\u0434\u043E\u0432\u0430\u043D\u0438\u044F \u0438\u043D\u0442\u0435\u0433\u0440\u0438\u0440\u0443\u0435\u043C\u043E\u0441\u0442\u0438 \u0432\u044B\u0440\u0430\u0436\u0435\u043D\u0438\u0439 \u0432 \u044D\u043B\u0435\u043C\u0435\u043D\u0442\u0430\u0440\u043D\u044B\u0445 \u0444\u0443\u043D\u043A\u0446\u0438\u044F\u0445 \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u0438\u043C\u0438 \u043C\u0435\u0442\u043E\u0434\u0430\u043C\u0438. \u041A\u043E\u043B\u044C\u0446\u043E, \u043F\u043E\u043B\u0435, \u0430\u043B\u0433\u0435\u0431\u0440\u0430, \u043E\u0441\u043D\u0430\u0449\u0451\u043D\u043D\u044B\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0440\u043E\u0432\u0430\u043D\u0438\u0435\u043C, \u043D\u0430\u0437\u044B\u0432\u0430\u044E\u0442\u0441\u044F \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u044B\u043C \u043A\u043E\u043B\u044C\u0446\u043E\u043C, \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u044B\u043C \u043F\u043E\u043B\u0435\u043C, \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u043E\u0439 \u0430\u043B\u0433\u0435\u0431\u0440\u043E\u0439, \u0441\u043E\u043E\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043D\u043D\u043E."@ru . . . . . . . . . "1109452073"^^ . . "( \uC774 \uBB38\uC11C\uB294 \uC5B4\uB5A4 \uC774\uD56D \uC5F0\uC0B0\uC5D0 \uB300\uD558\uC5EC \uACF1 \uADDC\uCE59\uC744 \uB530\uB974\uB294 \uC120\uD615 \uBCC0\uD658\uC73C\uB85C \uAD6C\uC131\uB41C \uB9AC \uB300\uC218\uC5D0 \uAD00\uD55C \uAC83\uC785\uB2C8\uB2E4. \uC0AC\uC2AC \uBCF5\uD569\uCCB4 \uAD6C\uC870\uB97C \uAC16\uB294 \uB9AC \uCD08\uB300\uC218\uC5D0 \uB300\uD574\uC11C\uB294 \uBBF8\uBD84 \uB4F1\uAE09 \uB9AC \uB300\uC218 \uBB38\uC11C\uB97C \uCC38\uACE0\uD558\uC2ED\uC2DC\uC624.) \uB9AC \uB300\uC218 \uC774\uB860\uC5D0\uC11C, \uBBF8\uBD84 \uB9AC \uB300\uC218(\u5FAE\u5206Lie\u4EE3\u6578, \uC601\uC5B4: derivation Lie algebra)\uB294 \uC5B4\uB5A4 \uC30D\uC120\uD615 \uC774\uD56D \uC5F0\uC0B0\uC5D0 \uB300\uD55C, \uACF1 \uADDC\uCE59\uC744 \uB530\uB974\uB294 \uBBF8\uBD84 \uC5F0\uC0B0\uB4E4\uB85C \uAD6C\uC131\uB41C \uB9AC \uB300\uC218\uC774\uB2E4.:A\u2162.117, \u00A7\u2162.10.2:383, Chapter 16:190, \u00A725 \uB300\uB7B5, \uC774 \uB300\uC218 \uAD6C\uC870\uC758 \uBB34\uD55C\uC18C \uC790\uAE30 \uB3D9\uD615\uC744 \uB098\uD0C0\uB0B8\uB2E4."@ko . "En alg\u00E8bre, le terme d\u00E9rivation est employ\u00E9 dans divers contextes pour d\u00E9signer une application v\u00E9rifiant l'identit\u00E9 de Leibniz. Selon le contexte, il peut s'agir, entre autres, d'une application additive d\u00E9finie sur un anneau A \u00E0 valeurs dans un -module, ou bien d'un endomorphisme d'une alg\u00E8bre unitaire sur un anneau unitaire. \n* Portail de l\u2019alg\u00E8bre"@fr . "Derivaci\u00F3n (\u00E1lgebra abstracta)"@es . . . . . . . "In mathematics, a derivation is a function on an algebra which generalizes certain features of the derivative operator. Specifically, given an algebra A over a ring or a field K, a K-derivation is a K-linear map D : A \u2192 A that satisfies Leibniz's law: More generally, if M is an A-bimodule, a K-linear map D : A \u2192 M that satisfies the Leibniz law is also called a derivation. The collection of all K-derivations of A to itself is denoted by DerK(A). The collection of K-derivations of A into an A-module M is denoted by DerK(A, M). Derivations occur in many different contexts in diverse areas of mathematics. The partial derivative with respect to a variable is an R-derivation on the algebra of real-valued differentiable functions on Rn. The Lie derivative with respect to a vector field is an R-derivation on the algebra of differentiable functions on a differentiable manifold; more generally it is a derivation on the tensor algebra of a manifold. It follows that the adjoint representation of a Lie algebra is a derivation on that algebra. The Pincherle derivative is an example of a derivation in abstract algebra. If the algebra A is noncommutative, then the commutator with respect to an element of the algebra A defines a linear endomorphism of A to itself, which is a derivation over K. That is, where is the commutator with respect to . An algebra A equipped with a distinguished derivation d forms a differential algebra, and is itself a significant object of study in areas such as differential Galois theory."@en . . . .