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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 Ramanujam–Samuel theorem ： ウィキペディア英語版 Ramanujam–Samuel theorem In algebraic geometry, the Ramanujam–Samuel theorem gives conditions for a divisor of a local ring to be principal. It was introduced independently by in answer to a question of Grothendieck and by C. P. Ramanujam in an appendix to a paper by , and was generalized by . ==Statement== Grothendieck's version of the Ramanujam–Samuel theorem is as follows. Suppose that ''A'' is a local Noetherian ring with maximal ideal ''m'', whose completion is integral and integrally closed, and ρ is a local homomorphism from ''A'' to a local Noetherian ring ''B'' of larger dimension such that ''B'' is formally smooth over ''A'' and the residue field of ''B'' is finite over that of ''A''. Then a cycle of codimension 1 in Spec(''B'') that is principal at the point ''mB'' is principal. 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「Ramanujam–Samuel theorem」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.