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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 Albert–Brauer–Hasse–Noether theorem ： ウィキペディア英語版 Albert–Brauer–Hasse–Noether theorem In algebraic number theory, the Albert–Brauer–Hasse–Noether theorem states that a central simple algebra over an algebraic number field ''K'' which splits over every completion ''K''''v'' is a matrix algebra over ''K''. The theorem is an example of a local-global principle in algebraic number theory and leads to a complete description of finite-dimensional division algebras over algebraic number fields in terms of their local invariants. It was proved independently by Helmut Hasse, Richard Brauer, and Emmy Noether and by Abraham Adrian Albert. == Statement of the theorem == Let ''A'' be a central simple algebra of rank ''d'' over an algebraic number field ''K''. Suppose that for any valuation ''v'', ''A'' splits over the corresponding local field ''K''''v'': : $A\backslash otimes\_K\; K\_v\; \backslash simeq\; M\_d(K\_v).$ Then ''A'' is isomorphic to the matrix algebra ''M''''d''(''K''). 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「Albert–Brauer–Hasse–Noether 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.