. "En matem\u00E0tiques, un element x d'un anell R es diu que \u00E9s nilpotent si existeix algun enter positiu n tal que xn = 0."@ca . "In mathematics, an element of a ring is called nilpotent if there exists some positive integer , called the index (or sometimes the degree), such that . The term was introduced by Benjamin Peirce in the context of his work on the classification of algebras."@en . . "Nilpotent"@nl . "\u0641\u064A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A\u060C \u064A\u0633\u0645\u0649 \u0639\u0646\u0635\u0631 \u0645\u0627 x \u0645\u0646 \u062D\u0644\u0642\u0629 R \u0639\u0646\u0635\u0631\u0627 \u0630\u0627 \u0642\u0648\u0629 \u0639\u0627\u062F\u0645\u0629 (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: Nilpotent)\u200F \u0625\u0630\u0627 \u0648\u062C\u062F \u0639\u062F\u062F \u0637\u0628\u064A\u0639\u064A n\u060C \u064A\u0633\u0645\u0649 \u0645\u0624\u0634\u0631 \u0647\u0630\u0627 \u0627\u0644\u0639\u0646\u0635\u0631\u060C \u0648\u0642\u062F \u064A\u0633\u0645\u0649 \u0623\u064A\u0636\u0627 \u062F\u0631\u062C\u062A\u0647\u060C \u062D\u064A\u062B xn = 0. \u064A\u0646\u0628\u063A\u064A \u062A\u0645\u064A\u064A\u0632 \u0647\u0630\u0627 \u0627\u0644\u0623\u0633 \u0639\u0646 \u0631\u062A\u0628\u0629 \u0627\u0644\u0639\u0646\u0635\u0631: \n* \u0644\u0627 \u064A\u0645\u0643\u0646 \u0627\u0644\u062D\u062F\u064A\u062B \u0639\u0646 \u0639\u0646\u0635\u0631 \u0630\u064A \u0642\u0648\u0629 \u0639\u0627\u062F\u0645\u0629 \u0625\u0630\u0627 \u0644\u0645 \u062A\u0645\u0643\u0646 \u0627\u0644\u0645\u062C\u0645\u0648\u0639\u0629 \u0627\u0644\u062A\u064A \u064A\u0646\u062A\u0645\u064A \u0625\u0644\u064A\u0647\u0627 \u0647\u0630\u0627 \u0627\u0644\u0639\u0646\u0635\u0631 \u062D\u0644\u0642\u0629. \u0627\u0644\u062D\u0644\u0642\u0629 \u062A\u064F\u0639\u0631\u0641 \u0628\u0639\u0645\u0644\u064A\u062A\u064A\u0646 \u0627\u062B\u0646\u062A\u064A\u0646. \u0639\u0645\u0644\u064A\u0629 \u0627\u0644\u0623\u0633 \u062A\u0642\u0627\u0645 \u0628\u0627\u0644\u0639\u0645\u0644\u064A\u0629 \u0627\u0644\u062B\u0627\u0646\u064A\u0629 (\u0627\u0644\u062C\u062F\u0627\u0621)\u060C \u0628\u064A\u0646\u0645\u0627 \u0627\u0644\u0646\u062A\u064A\u062C\u0629 \u0647\u064A \u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u062D\u0627\u064A\u062F \u0644\u0644\u0639\u0645\u0644\u064A\u0629 \u0627\u0644\u0623\u0648\u0644\u0649 (\u0627\u0644\u062C\u0645\u0639). \n* \u064A\u0645\u0643\u0646 \u0627\u0644\u062D\u062F\u064A\u062B \u0639\u0646 \u0631\u062A\u0628\u0629 \u0639\u0646\u0635\u0631 \u062D\u062A\u0649 \u0625\u0630\u0627 \u0643\u0627\u0646\u062A \u0627\u0644\u0645\u062C\u0645\u0648\u0639\u0629 \u0627\u0644\u062A\u064A \u064A\u0646\u062A\u0645\u064A \u0625\u0644\u064A\u0647\u0627 \u0630\u0644\u0643 \u0627\u0644\u0639\u0646\u0635\u0631 \u0644\u064A\u0633\u062A \u0628\u062D\u0644\u0642\u0629. \u064A\u0643\u0641\u064A \u0623\u0646 \u062A\u0643\u0648\u0646 \u0632\u0645\u0631\u0629. \u0627\u0644\u0639\u0645\u0644\u064A\u0629 \u0627\u0644\u062A\u064A \u064A\u0642\u0627\u0645 \u0628\u0647\u0627 \u0627\u0644\u0623\u0633 \u0647\u064A \u0627\u0644\u0639\u0645\u0644\u064A\u0629 \u0627\u0644\u0645\u0639\u0631\u0641\u0629 \u0644\u0644\u0632\u0645\u0631\u0629 \u0648\u0627\u0644\u0646\u062A\u064A\u062C\u0629 \u0647\u064A \u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u062D\u0627\u064A\u062F \u0644\u0644\u0639\u0645\u0644\u064A\u0629 \u0627\u0644\u0645\u0639\u0631\u0641\u0629 \u0644\u0644\u0632\u0645\u0631\u0629 \u0630\u0627\u062A\u0647\u0627."@ar . "\u041D\u0438\u043B\u044C\u043F\u043E\u0442\u0435\u043D\u0442\u043D\u044B\u0439 \u044D\u043B\u0435\u043C\u0435\u043D\u0442 \u2014 \u044D\u043B\u0435\u043C\u0435\u043D\u0442 \u043A\u043E\u043B\u044C\u0446\u0430, \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u0430\u044F \u0441\u0442\u0435\u043F\u0435\u043D\u044C \u043A\u043E\u0442\u043E\u0440\u043E\u0433\u043E \u043E\u0431\u0440\u0430\u0449\u0430\u0435\u0442\u0441\u044F \u0432 \u043D\u043E\u043B\u044C. \u0420\u0430\u0441\u0441\u043C\u043E\u0442\u0440\u0435\u043D\u0438\u0435 \u043D\u0438\u043B\u044C\u043F\u043E\u0442\u0435\u043D\u0442\u043D\u044B\u0445 \u044D\u043B\u0435\u043C\u0435\u043D\u0442\u043E\u0432 \u0447\u0430\u0441\u0442\u043E \u043E\u043A\u0430\u0437\u044B\u0432\u0430\u0435\u0442\u0441\u044F \u043F\u043E\u043B\u0435\u0437\u043D\u044B\u043C \u0432 \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u043E\u0439 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0438, \u0442\u0430\u043A \u043A\u0430\u043A \u043E\u043D\u0438 \u043F\u043E\u0437\u0432\u043E\u043B\u044F\u044E\u0442 \u043F\u043E\u043B\u0443\u0447\u0438\u0442\u044C \u0447\u0438\u0441\u0442\u043E \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u0438\u0435 \u0430\u043D\u0430\u043B\u043E\u0433\u0438 \u0440\u044F\u0434\u0430 \u043F\u043E\u043D\u044F\u0442\u0438\u0439, \u0442\u0438\u043F\u0438\u0447\u043D\u044B\u0445 \u0434\u043B\u044F \u0430\u043D\u0430\u043B\u0438\u0437\u0430 \u0438 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u043E\u0439 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0438 (\u0431\u0435\u0441\u043A\u043E\u043D\u0435\u0447\u043D\u043E \u043C\u0430\u043B\u044B\u0435 \u0434\u0435\u0444\u043E\u0440\u043C\u0430\u0446\u0438\u0438 \u0438 \u0442. \u043F.). \u0422\u0435\u0440\u043C\u0438\u043D \u0432\u0432\u0451\u043B \u0411\u0435\u043D\u0434\u0436\u0430\u043C\u0438\u043D \u041F\u0438\u0440\u0441 \u0432 \u0440\u0430\u0431\u043E\u0442\u0435 \u043F\u043E \u043A\u043B\u0430\u0441\u0441\u0438\u0444\u0438\u043A\u0430\u0446\u0438\u0438 \u0430\u043B\u0433\u0435\u0431\u0440."@ru . . "\u5E42\u96F6\u5143"@zh . "Nilpotentn\u00ED prvek je v matematice takov\u00FD prvek okruhu , u kter\u00E9ho pro n\u011Bjak\u00E9 p\u0159irozen\u00E9 \u010D\u00EDslo plat\u00ED , tedy jeho\u017E n\u011Bjak\u00E1 kone\u010Dn\u00E1 mocnina je rovna nulov\u00E9mu prvku."@cs . . "In de wiskunde wordt een element x van een ring R nilpotent genoemd als er een zeker positief geheel getal n bestaat zodat x tot de macht n gelijk is aan nul ."@nl . "En matem\u00E1tica, un elemento x de un anillo R se dice que es nilpotente si existe alg\u00FAn entero positivo n tal que xn = 0."@es . "Nilpotent"@fr . . . "En math\u00E9matiques, un \u00E9l\u00E9ment x d'un anneau unitaire (ou m\u00EAme d'un pseudo-anneau) est dit nilpotent s'il existe un entier naturel n non nul tel que xn = 0."@fr . . . . . "Element nilpotentny"@pl . "Nilpotenteco"@eo . . . . . . "In matematica, e in particolare in algebra, l'aggettivo nilpotente serve per caratterizzare vari tipi di entit\u00E0. Per elemento nilpotente di un anello si intende un elemento non nullo tale che esiste un intero positivo per il quale . Per gruppo nilpotente si intende un gruppo tale che la catena di gruppi con centro di , termina finitamente. Un gruppo di Lie nilpotente \u00E8 un gruppo di Lie che possiede un gruppo ricoprente semplicemente connesso omeomorfo a uno spazio reale di dimensione finita interpretato come gruppo di Lie."@it . . . "Nilpotent"@en . . . . "En math\u00E9matiques, un \u00E9l\u00E9ment x d'un anneau unitaire (ou m\u00EAme d'un pseudo-anneau) est dit nilpotent s'il existe un entier naturel n non nul tel que xn = 0."@fr . . . "Element nilpotentny lub nilpotent pier\u015Bcienia \u2013 element pier\u015Bcienia o tej w\u0142asno\u015Bci, \u017Ce dla pewnej liczby naturalnej zachodzi: . W ka\u017Cdym pier\u015Bcieniu 0 (element neutralny dodawania) jest elementem nilpotentnym."@pl . "En matem\u00E0tiques, un element x d'un anell R es diu que \u00E9s nilpotent si existeix algun enter positiu n tal que xn = 0."@ca . "\u041D\u0456\u043B\u044C\u043F\u043E\u0442\u0435\u043D\u0442\u043D\u0438\u0439 \u0435\u043B\u0435\u043C\u0435\u043D\u0442 \u0430\u0431\u043E \u043D\u0456\u043B\u044C\u043F\u043E\u0442\u0435\u043D\u0442 \u2014 \u0435\u043B\u0435\u043C\u0435\u043D\u0442 \u043A\u0456\u043B\u044C\u0446\u044F, \u0449\u043E \u0437\u0430\u0434\u043E\u0432\u043E\u043B\u044C\u043D\u044F\u0454 \u0440\u0456\u0432\u043D\u043E\u0441\u0442\u0456 \u0434\u043B\u044F \u0434\u0435\u044F\u043A\u043E\u0433\u043E \u043D\u0430\u0442\u0443\u0440\u0430\u043B\u044C\u043D\u043E\u0433\u043E . \u041C\u0456\u043D\u0456\u043C\u0430\u043B\u044C\u043D\u0435 \u0437\u043D\u0430\u0447\u0435\u043D\u043D\u044F , \u0434\u043B\u044F \u044F\u043A\u043E\u0433\u043E \u0441\u043F\u0440\u0430\u0432\u0435\u0434\u043B\u0438\u0432\u0430 \u0446\u044F \u0440\u0456\u0432\u043D\u0456\u0441\u0442\u044C, \u043D\u0430\u0437\u0438\u0432\u0430\u0454\u0442\u044C\u0441\u044F \u0456\u043D\u0434\u0435\u043A\u0441\u043E\u043C \u043D\u0456\u043B\u044C\u043F\u043E\u0442\u0435\u043D\u0442\u043D\u043E\u0441\u0442\u0456 \u0435\u043B\u0435\u043C\u0435\u043D\u0442\u0443 ."@uk . "\uBA71\uC601\uC6D0(\u51AA\u96F6\u5143, \uC601\uC5B4: nilpotent element)\uC740 \uAC70\uB4ED\uC81C\uACF1\uD558\uC5EC 0\uC774 \uB418\uB294, \uD658\uC758 \uC6D0\uC18C\uB2E4."@ko . . . . . . . . "\u041D\u0438\u043B\u044C\u043F\u043E\u0442\u0435\u043D\u0442\u043D\u044B\u0439 \u044D\u043B\u0435\u043C\u0435\u043D\u0442 \u2014 \u044D\u043B\u0435\u043C\u0435\u043D\u0442 \u043A\u043E\u043B\u044C\u0446\u0430, \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u0430\u044F \u0441\u0442\u0435\u043F\u0435\u043D\u044C \u043A\u043E\u0442\u043E\u0440\u043E\u0433\u043E \u043E\u0431\u0440\u0430\u0449\u0430\u0435\u0442\u0441\u044F \u0432 \u043D\u043E\u043B\u044C. \u0420\u0430\u0441\u0441\u043C\u043E\u0442\u0440\u0435\u043D\u0438\u0435 \u043D\u0438\u043B\u044C\u043F\u043E\u0442\u0435\u043D\u0442\u043D\u044B\u0445 \u044D\u043B\u0435\u043C\u0435\u043D\u0442\u043E\u0432 \u0447\u0430\u0441\u0442\u043E \u043E\u043A\u0430\u0437\u044B\u0432\u0430\u0435\u0442\u0441\u044F \u043F\u043E\u043B\u0435\u0437\u043D\u044B\u043C \u0432 \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u043E\u0439 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0438, \u0442\u0430\u043A \u043A\u0430\u043A \u043E\u043D\u0438 \u043F\u043E\u0437\u0432\u043E\u043B\u044F\u044E\u0442 \u043F\u043E\u043B\u0443\u0447\u0438\u0442\u044C \u0447\u0438\u0441\u0442\u043E \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u0438\u0435 \u0430\u043D\u0430\u043B\u043E\u0433\u0438 \u0440\u044F\u0434\u0430 \u043F\u043E\u043D\u044F\u0442\u0438\u0439, \u0442\u0438\u043F\u0438\u0447\u043D\u044B\u0445 \u0434\u043B\u044F \u0430\u043D\u0430\u043B\u0438\u0437\u0430 \u0438 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u043E\u0439 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0438 (\u0431\u0435\u0441\u043A\u043E\u043D\u0435\u0447\u043D\u043E \u043C\u0430\u043B\u044B\u0435 \u0434\u0435\u0444\u043E\u0440\u043C\u0430\u0446\u0438\u0438 \u0438 \u0442. \u043F.). \u0422\u0435\u0440\u043C\u0438\u043D \u0432\u0432\u0451\u043B \u0411\u0435\u043D\u0434\u0436\u0430\u043C\u0438\u043D \u041F\u0438\u0440\u0441 \u0432 \u0440\u0430\u0431\u043E\u0442\u0435 \u043F\u043E \u043A\u043B\u0430\u0441\u0441\u0438\u0444\u0438\u043A\u0430\u0446\u0438\u0438 \u0430\u043B\u0433\u0435\u0431\u0440."@ru . . . . . . . "\uBA71\uC601\uC6D0"@ko . "\u0639\u0646\u0635\u0631 \u0630\u0648 \u0642\u0648\u0629 \u0639\u0627\u062F\u0645\u0629"@ar . . . "\u041D\u0456\u043B\u044C\u043F\u043E\u0442\u0435\u043D\u0442\u043D\u0438\u0439 \u0435\u043B\u0435\u043C\u0435\u043D\u0442"@uk . . . "In de wiskunde wordt een element x van een ring R nilpotent genoemd als er een zeker positief geheel getal n bestaat zodat x tot de macht n gelijk is aan nul ."@nl . . . . . "\u0641\u064A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A\u060C \u064A\u0633\u0645\u0649 \u0639\u0646\u0635\u0631 \u0645\u0627 x \u0645\u0646 \u062D\u0644\u0642\u0629 R \u0639\u0646\u0635\u0631\u0627 \u0630\u0627 \u0642\u0648\u0629 \u0639\u0627\u062F\u0645\u0629 (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: Nilpotent)\u200F \u0625\u0630\u0627 \u0648\u062C\u062F \u0639\u062F\u062F \u0637\u0628\u064A\u0639\u064A n\u060C \u064A\u0633\u0645\u0649 \u0645\u0624\u0634\u0631 \u0647\u0630\u0627 \u0627\u0644\u0639\u0646\u0635\u0631\u060C \u0648\u0642\u062F \u064A\u0633\u0645\u0649 \u0623\u064A\u0636\u0627 \u062F\u0631\u062C\u062A\u0647\u060C \u062D\u064A\u062B xn = 0. \u064A\u0646\u0628\u063A\u064A \u062A\u0645\u064A\u064A\u0632 \u0647\u0630\u0627 \u0627\u0644\u0623\u0633 \u0639\u0646 \u0631\u062A\u0628\u0629 \u0627\u0644\u0639\u0646\u0635\u0631: \n* \u0644\u0627 \u064A\u0645\u0643\u0646 \u0627\u0644\u062D\u062F\u064A\u062B \u0639\u0646 \u0639\u0646\u0635\u0631 \u0630\u064A \u0642\u0648\u0629 \u0639\u0627\u062F\u0645\u0629 \u0625\u0630\u0627 \u0644\u0645 \u062A\u0645\u0643\u0646 \u0627\u0644\u0645\u062C\u0645\u0648\u0639\u0629 \u0627\u0644\u062A\u064A \u064A\u0646\u062A\u0645\u064A \u0625\u0644\u064A\u0647\u0627 \u0647\u0630\u0627 \u0627\u0644\u0639\u0646\u0635\u0631 \u062D\u0644\u0642\u0629. \u0627\u0644\u062D\u0644\u0642\u0629 \u062A\u064F\u0639\u0631\u0641 \u0628\u0639\u0645\u0644\u064A\u062A\u064A\u0646 \u0627\u062B\u0646\u062A\u064A\u0646. \u0639\u0645\u0644\u064A\u0629 \u0627\u0644\u0623\u0633 \u062A\u0642\u0627\u0645 \u0628\u0627\u0644\u0639\u0645\u0644\u064A\u0629 \u0627\u0644\u062B\u0627\u0646\u064A\u0629 (\u0627\u0644\u062C\u062F\u0627\u0621)\u060C \u0628\u064A\u0646\u0645\u0627 \u0627\u0644\u0646\u062A\u064A\u062C\u0629 \u0647\u064A \u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u062D\u0627\u064A\u062F \u0644\u0644\u0639\u0645\u0644\u064A\u0629 \u0627\u0644\u0623\u0648\u0644\u0649 (\u0627\u0644\u062C\u0645\u0639). \n* \u064A\u0645\u0643\u0646 \u0627\u0644\u062D\u062F\u064A\u062B \u0639\u0646 \u0631\u062A\u0628\u0629 \u0639\u0646\u0635\u0631 \u062D\u062A\u0649 \u0625\u0630\u0627 \u0643\u0627\u0646\u062A \u0627\u0644\u0645\u062C\u0645\u0648\u0639\u0629 \u0627\u0644\u062A\u064A \u064A\u0646\u062A\u0645\u064A \u0625\u0644\u064A\u0647\u0627 \u0630\u0644\u0643 \u0627\u0644\u0639\u0646\u0635\u0631 \u0644\u064A\u0633\u062A \u0628\u062D\u0644\u0642\u0629. \u064A\u0643\u0641\u064A \u0623\u0646 \u062A\u0643\u0648\u0646 \u0632\u0645\u0631\u0629. \u0627\u0644\u0639\u0645\u0644\u064A\u0629 \u0627\u0644\u062A\u064A \u064A\u0642\u0627\u0645 \u0628\u0647\u0627 \u0627\u0644\u0623\u0633 \u0647\u064A \u0627\u0644\u0639\u0645\u0644\u064A\u0629 \u0627\u0644\u0645\u0639\u0631\u0641\u0629 \u0644\u0644\u0632\u0645\u0631\u0629 \u0648\u0627\u0644\u0646\u062A\u064A\u062C\u0629 \u0647\u064A \u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u062D\u0627\u064A\u062F \u0644\u0644\u0639\u0645\u0644\u064A\u0629 \u0627\u0644\u0645\u0639\u0631\u0641\u0629 \u0644\u0644\u0632\u0645\u0631\u0629 \u0630\u0627\u062A\u0647\u0627."@ar . . "Nilpotentn\u00ED prvek"@cs . "Nilpotente"@es . "\u041D\u0438\u043B\u044C\u043F\u043E\u0442\u0435\u043D\u0442\u043D\u044B\u0439 \u044D\u043B\u0435\u043C\u0435\u043D\u0442"@ru . . . "\u6570\u5B66\u306B\u304A\u3044\u3066\u3001\u74B0 R \u306E\u5143 x \u306F\u3042\u308B\u6B63\u306E\u6574\u6570 n \u304C\u5B58\u5728\u3057\u3066 xn = 0 \u3068\u306A\u308B\u3068\u304D\u306B\u51AA\u96F6\u5143\uFF08\u3079\u304D\u308C\u3044\u3052\u3093\u3001\u82F1: nilpotent element\uFF09\u3068\u3044\u3046\u3002 \u51AA\u96F6 (nilpotent) \u3068\u3044\u3046\u8A00\u8449\u306F\u3001\u30D9\u30F3\u30B8\u30E3\u30DF\u30F3\u30FB\u30D1\u30FC\u30B9\u306B\u3088\u3063\u3066\u3001\u591A\u5143\u74B0\u306E\u5143\u306E\u3042\u308B\u51AA\u304C 0 \u306B\u306A\u308B\u3068\u3044\u3046\u6587\u8108\u30671870\u5E74\u9803\u306B\u5C0E\u5165\u3055\u308C\u305F\u3002"@ja . . . "Nilpotente"@it . "Element nilpotentny lub nilpotent pier\u015Bcienia \u2013 element pier\u015Bcienia o tej w\u0142asno\u015Bci, \u017Ce dla pewnej liczby naturalnej zachodzi: . W ka\u017Cdym pier\u015Bcieniu 0 (element neutralny dodawania) jest elementem nilpotentnym."@pl . . . "Nilpotente"@pt . "Nilpot\u00E8ncia"@ca . . . . "\u041D\u0456\u043B\u044C\u043F\u043E\u0442\u0435\u043D\u0442\u043D\u0438\u0439 \u0435\u043B\u0435\u043C\u0435\u043D\u0442 \u0430\u0431\u043E \u043D\u0456\u043B\u044C\u043F\u043E\u0442\u0435\u043D\u0442 \u2014 \u0435\u043B\u0435\u043C\u0435\u043D\u0442 \u043A\u0456\u043B\u044C\u0446\u044F, \u0449\u043E \u0437\u0430\u0434\u043E\u0432\u043E\u043B\u044C\u043D\u044F\u0454 \u0440\u0456\u0432\u043D\u043E\u0441\u0442\u0456 \u0434\u043B\u044F \u0434\u0435\u044F\u043A\u043E\u0433\u043E \u043D\u0430\u0442\u0443\u0440\u0430\u043B\u044C\u043D\u043E\u0433\u043E . \u041C\u0456\u043D\u0456\u043C\u0430\u043B\u044C\u043D\u0435 \u0437\u043D\u0430\u0447\u0435\u043D\u043D\u044F , \u0434\u043B\u044F \u044F\u043A\u043E\u0433\u043E \u0441\u043F\u0440\u0430\u0432\u0435\u0434\u043B\u0438\u0432\u0430 \u0446\u044F \u0440\u0456\u0432\u043D\u0456\u0441\u0442\u044C, \u043D\u0430\u0437\u0438\u0432\u0430\u0454\u0442\u044C\u0441\u044F \u0456\u043D\u0434\u0435\u043A\u0441\u043E\u043C \u043D\u0456\u043B\u044C\u043F\u043E\u0442\u0435\u043D\u0442\u043D\u043E\u0441\u0442\u0456 \u0435\u043B\u0435\u043C\u0435\u043D\u0442\u0443 ."@uk . "\uBA71\uC601\uC6D0(\u51AA\u96F6\u5143, \uC601\uC5B4: nilpotent element)\uC740 \uAC70\uB4ED\uC81C\uACF1\uD558\uC5EC 0\uC774 \uB418\uB294, \uD658\uC758 \uC6D0\uC18C\uB2E4."@ko . . . . "Em matem\u00E1tica, um elemento x de um anel \u00E9 nilpotente quando existe algum n\u00FAmero natural n tal que ."@pt . . . "En matem\u00E1tica, un elemento x de un anillo R se dice que es nilpotente si existe alg\u00FAn entero positivo n tal que xn = 0."@es . . . . "In mathematics, an element of a ring is called nilpotent if there exists some positive integer , called the index (or sometimes the degree), such that . The term was introduced by Benjamin Peirce in the context of his work on the classification of algebras."@en . . "Nilpotenteco estas termino el algebro, precipe el la teorio de ringoj. Elemento de ringo estas nilpotenta, se ekzistas pozitiva natura nombro tiel, ke . Idealo de estas nilpotenta, se ekzistas pozitiva natura nombro tiel, ke ."@eo . . "1124305472"^^ . . . . . . . . . . . "Ein nilpotentes Element ist ein Begriff aus der Ringtheorie, einem Teilgebiet der Mathematik. Ein Element eines Rings hei\u00DFt nilpotent, wenn es gen\u00FCgend oft mit sich selbst multipliziert das Nullelement ergibt."@de . "\u51AA\u96F6\u5143"@ja . . . . "\u5728\u62BD\u8C61\u4EE3\u6570\u4E2D\uFF0C\u67D0\u4E2A\u73AFR\u7684\u4E00\u4E2A\u5143\u7D20x\u662F\u4E00\u4E2A\u5E42\u96F6\u5143\uFF0C\u5F53\u5B58\u5728\u4E00\u4E2A\u6B63\u6574\u6570n\uFF0C\u4F7F\u5F97xn\u7B49\u4E8E\u52A0\u6CD5\u4E2D\u7684\u96F6\u5143\u7D20\u3002"@zh . . . . . . . . . "Nilpotentn\u00ED prvek je v matematice takov\u00FD prvek okruhu , u kter\u00E9ho pro n\u011Bjak\u00E9 p\u0159irozen\u00E9 \u010D\u00EDslo plat\u00ED , tedy jeho\u017E n\u011Bjak\u00E1 kone\u010Dn\u00E1 mocnina je rovna nulov\u00E9mu prvku."@cs . "Ein nilpotentes Element ist ein Begriff aus der Ringtheorie, einem Teilgebiet der Mathematik. Ein Element eines Rings hei\u00DFt nilpotent, wenn es gen\u00FCgend oft mit sich selbst multipliziert das Nullelement ergibt."@de . . . "252235"^^ . "7686"^^ . . . . . "Nilpotentes Element"@de . . . "Nilpotenteco estas termino el algebro, precipe el la teorio de ringoj. Elemento de ringo estas nilpotenta, se ekzistas pozitiva natura nombro tiel, ke . Idealo de estas nilpotenta, se ekzistas pozitiva natura nombro tiel, ke ."@eo . . . . . "\u5728\u62BD\u8C61\u4EE3\u6570\u4E2D\uFF0C\u67D0\u4E2A\u73AFR\u7684\u4E00\u4E2A\u5143\u7D20x\u662F\u4E00\u4E2A\u5E42\u96F6\u5143\uFF0C\u5F53\u5B58\u5728\u4E00\u4E2A\u6B63\u6574\u6570n\uFF0C\u4F7F\u5F97xn\u7B49\u4E8E\u52A0\u6CD5\u4E2D\u7684\u96F6\u5143\u7D20\u3002"@zh . . . . "In matematica, e in particolare in algebra, l'aggettivo nilpotente serve per caratterizzare vari tipi di entit\u00E0. Per elemento nilpotente di un anello si intende un elemento non nullo tale che esiste un intero positivo per il quale . Per gruppo nilpotente si intende un gruppo tale che la catena di gruppi con centro di , termina finitamente. Un gruppo di Lie nilpotente \u00E8 un gruppo di Lie che possiede un gruppo ricoprente semplicemente connesso omeomorfo a uno spazio reale di dimensione finita interpretato come gruppo di Lie. Una matrice quadrata si dice matrice nilpotente se ha tutti gli autovalori nulli; essa risulta anche elemento nilpotente dell'anello delle matrici quadrate. Con il termine nilpotenza si intende la propriet\u00E0, di un elemento di un anello, di un gruppo, di una matrice, ecc. dell'essere nilpotente."@it . . "Em matem\u00E1tica, um elemento x de um anel \u00E9 nilpotente quando existe algum n\u00FAmero natural n tal que ."@pt . . "\u6570\u5B66\u306B\u304A\u3044\u3066\u3001\u74B0 R \u306E\u5143 x \u306F\u3042\u308B\u6B63\u306E\u6574\u6570 n \u304C\u5B58\u5728\u3057\u3066 xn = 0 \u3068\u306A\u308B\u3068\u304D\u306B\u51AA\u96F6\u5143\uFF08\u3079\u304D\u308C\u3044\u3052\u3093\u3001\u82F1: nilpotent element\uFF09\u3068\u3044\u3046\u3002 \u51AA\u96F6 (nilpotent) \u3068\u3044\u3046\u8A00\u8449\u306F\u3001\u30D9\u30F3\u30B8\u30E3\u30DF\u30F3\u30FB\u30D1\u30FC\u30B9\u306B\u3088\u3063\u3066\u3001\u591A\u5143\u74B0\u306E\u5143\u306E\u3042\u308B\u51AA\u304C 0 \u306B\u306A\u308B\u3068\u3044\u3046\u6587\u8108\u30671870\u5E74\u9803\u306B\u5C0E\u5165\u3055\u308C\u305F\u3002"@ja .