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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 Analytically irreducible ring ： ウィキペディア英語版 Analytically irreducible ring In algebra, an analytically irreducible ring is a local ring whose completion has no zero divisors. Geometrically this corresponds to a variety with only one analytic branch at a point. proved that if a local ring of an algebraic variety is a normal ring, then it is analytically irreducible. There are many examples of reduced and irreducible local rings that are analytically reducible, such as the local ring of a node of an irreducible curve, but it is hard to find examples that are also normal. gave such an example of a normal Noetherian local ring that is analytically reducible. ==Nagata's example== Suppose that ''K'' is a field of characteristic not 2, and ''K''  is the formal power series ring over ''K'' in 2 variables. Let ''R'' be the subring of ''K''  generated by ''x'', ''y'', and the elements ''z''''n'' and localized at these elements, where :$w=\backslash sum\_\; a\_mx^m$ is transcendental over ''K''(''x'') :$z\_1=(y+w)^2$ :$z\_=(z\_1-(y+\backslash sum\_a\_mx^m)^2)/x^n$. Then ''R''()/(''X'' 2–''z''1) is a normal Noetherian local ring that is analytically reducible. 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「Analytically irreducible ring」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.