翻訳と辞書 Words near each other ・ 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 ・ Nils (album) 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 algebra (ring theory) ： ウィキペディア英語版 Nilpotent algebra (ring theory) In mathematics, specifically in ring theory, a nilpotent algebra over a commutative ring is an algebra over a commutative ring, in which for some positive integer ''n'' every product containing at least ''n'' elements of the algebra is zero. The concept of a nilpotent Lie algebra has a different definition, which depends upon the Lie bracket. (There is no Lie bracket for many algebras over commutative rings; a Lie algebra involves its Lie bracket, whereas, there is no Lie bracket defined in the general case of an algebra over a commutative ring.) Another possible source of confusion in terminology is the ''quantum nilpotent algebra'', a concept related to quantum groups and Hopf algebras. ==Formal definition== An associative algebra $A$ over a commutative ring $R$ is defined to be a nilpotent algebra if and only if there exists some positive integer $n$ such that $0=y\_1\backslash \; y\_2\backslash \; \backslash cdots\backslash \; y\_n$ for all $y\_1,\; \backslash \; y\_2,\; \backslash \; \backslash ldots,\backslash \; y\_n$ in the algebra $A$. The smallest such $n$ is called the index of the algebra $A$. In the case of a non-associative algebra, the definition is that every different multiplicative association of the $n$ elements is zero. 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 algebra (ring theory)」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.