翻訳と辞書 Words near each other ・ Artistic Creation ・ Artistic cycling ・ Artistic depictions of the Bangladesh Liberation War ・ Artistic depictions of the Bengali Language Movement ・ Artistic depictions of the partition of India ・ Artin Madoyan ・ Artin Penik ・ Artin Poturlyan ・ Artin reciprocity law ・ Artin transfer (group theory) ・ Artin's conjecture on primitive roots ・ Artine Artinian ・ Artines ・ Artington ・ Artinian ・ Artinian ideal ・ Artinian module ・ Artinian ring ・ Artinite ・ Artins ・ ArtInsights ・ Artinskian ・ Artinsky District ・ Artin–Hasse exponential ・ Artin–Mazur zeta function ・ Artin–Rees lemma ・ Artin–Schreier curve ・ Artin–Schreier theory ・ Artin–Tate lemma ・ Artin–Verdier duality 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 Artinian ideal ： ウィキペディア英語版 Artinian ideal In abstract algebra, an Artinian ideal, named after Emil Artin, is encountered in ring theory, in particular, with polynomial rings. Given a polynomial ring ''R'' = ''k''() where ''k'' is some field, an Artinian ideal is an ideal ''I'' in ''R'' for which the Krull dimension of the quotient ring ''R''/''I'' is 0. Also, less precisely, one can think of an Artinian ideal as one that has at least each indeterminate in ''R'' raised to a power greater than 0 as a generator. If an ideal is not Artinian, one can take the Artinian closure of it as follows. First, take the least common multiple of the generators of the ideal. Second, add to the generating set of the ideal each indeterminate of the LCM with its power increased by 1 if the power is not 0 to begin with. An example is below. ==Examples== Let $R\; =\; k()$, and let $I\; =\; (x^2,y^5,z^4),\; \backslash ;\; J\; =\; (x^3,\; y^2,\; z^6,\; x^2yz^4,\; yz^3)$ and $\backslash displaystyle$. Here, $\backslash displaystyle$ and $\backslash displaystyle$ are Artinian ideals, but $\backslash displaystyle$ is not because in $\backslash displaystyle$, the indeterminate $\backslash displaystyle$ does not appear alone to a power as a generator. To take the Artinian closure of $\backslash displaystyle$, $\backslash displaystyle$, which is $\backslash displaystyle$. Then, we add the generators $\backslash displaystyle$, and $\backslash displaystyle$ to $\backslash displaystyle$, and reduce. Thus, we have $\backslash displaystyle\{\backslash hat\{K\}\}\; =\; (x^3,\; y^4,\; z^8,\; x^2z^7)$ which is Artinian. 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「Artinian ideal」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.