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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 Formally smooth map ： ウィキペディア英語版 Formally smooth map In algebraic geometry and commutative algebra, a ring homomorphism $f:A\backslash to\; B$ is called formally smooth (from French: ''Formellement lisse'') if it satisfies the following infinitesimal lifting property: Suppose ''B'' is given the structure of an ''A''-algebra via the map ''f''. Given a commutative ''A''-algebra, ''C'', and a nilpotent ideal $N\backslash subseteq\; C$, any ''A''-algebra homomorphism $B\backslash to\; C/N$ may be lifted to an ''A''-algebra map $B\; \backslash to\; C$. If moreover any such lifting is unique, then ''f'' is said to be formally étale. Formally smooth maps were defined by Alexander Grothendieck in ''Éléments de géométrie algébrique'' IV. For finitely presented morphisms, formal smoothness is equivalent to usual notion of smoothness. ==References== 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「Formally smooth map」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.