| 翻訳と辞書 |
| Popescu’s theorem ： ウィキペディア英語版 |
Popescu’s theorem
In algebra, Popescu’s theorem, introduced by D. Popescu, states:
:Let ''A'' be a noetherian ring and ''B'' a noetherian algebra over it. Then, the structure map ''A'' →''B'' is a regular morphism if and only if ''B'' is a direct limit of smooth ''A''-algebras.
For example, if ''A'' is a local G-ring (e.g., local excellent ring) and ''B'' its completion, then the map ''A'' →''B'' is regular by definition and the theorem applies.
The usual proof of the Artin approximation theorem relies crucially on Popescu's theorem.
== 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「Popescu’s 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.
|
|