翻訳と辞書 Words near each other ・ Nils Gregoriussen Skilbred ・ Nils Grevillius ・ Nils Grönvall ・ Nils Gude ・ Nils Gunnar Lie ・ Nils Gustaf Ekholm ・ Nils Gustaf Nordenskiöld ・ Nils Gustafsson ・ Nilphamari Government High School ・ Nilphamari Sadar Upazila ・ Nilphamari Stadium ・ Nilphamari-1 (Jatiyo Sangshad constituency) ・ Nilphamari-2 (Jatiyo Sangshad constituency) ・ Nilphamari-3 (Jatiyo Sangshad constituency) ・ Nilpotence theorem ・ Nilpotent ・ Nilpotent algebra (ring theory) ・ Nilpotent cone ・ Nilpotent group ・ Nilpotent ideal ・ Nilpotent Lie algebra ・ Nilpotent matrix ・ Nilpotent operator ・ Nilpotent orbit ・ Nilpotent space ・ Nilradical ・ Nilradical of a Lie algebra ・ Nilradical of a ring ・ Nilratan Sircar ・ Nils Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Nilpotent ： ウィキペディア英語版 Nilpotent In mathematics, an element, ''x'', of a ring, ''R'', is called nilpotent if there exists some positive integer, ''n'', such that ''x''''n'' = 0. The term was introduced by Benjamin Peirce in the context of his work on the classification of algebras.〔Polcino Milies & Sehgal (2002), ''An Introduction to Group Rings''. p. 127.〕 == Examples == *This definition can be applied in particular to square matrices. The matrix :: $A\; =\; \backslash begin$ 0 & 1 & 0\\ 0 & 0 & 1\\ 0 & 0 & 0 \end :is nilpotent because ''A''3 = 0. See nilpotent matrix for more. * In the factor ring Z/9Z, the equivalence class of 3 is nilpotent because 32 is congruent to 0 modulo 9. * Assume that two elements ''a'', ''b'' in a (non-commutative) ring ''R'' satisfy ''ab'' = 0. Then the element ''c'' = ''ba'' is nilpotent (if non-zero) as ''c''2 = (''ba'')2 = ''b''(''ab'')''a'' = 0. An example with matrices (for ''a'', ''b''): :: $A\; =\; \backslash begin$ 0 & 1\\ 0 & 1 \end, \;\; B =\begin 0 & 1\\ 0 & 0 \end. : Here ''AB'' = 0, ''BA'' = ''B''. *The ring of coquaternions contains a cone of nilpotents. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Nilpotent」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.