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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Symbolic power of a prime ideal ： ウィキペディア英語版 Symbolic power of a prime ideal In algebra, given a ring ''R'' and a prime ideal ''P'' in it, the ''n''-th symbolic power of ''P'' is the ideal :$P^\; =\; P^n\; R\_P\; \backslash cap\; R\; =\; \backslash .$〔Here, by abuse of notation, we write $I\; \backslash cap\; R$ to mean the pre-image of ''I'' along the localization map $R\; \backslash to\; R\_P$.〕 It is the smallest ''P''-primary ideal containing the ''n''-th power ''P''''n''. Very roughly, it consists of functions with zeros of order ''n'' along the variety defined by ''P''. If ''R'' is Noetherian, then it is the ''P''-primary component in the primary decomposition of ''P''''n''. We have: $P^\; =\; P$ and if ''P'' is a maximal ideal, then $P^\; =\; P^n$. == References == *http://www.math.lsa.umich.edu/~hochster/711F07/L09.07.pdf 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「Symbolic power of a prime 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.