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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 Gelfand–Kirillov dimension ： ウィキペディア英語版 Gelfand–Kirillov dimension In algebra, the Gelfand–Kirillov dimension (or GK dimension) of a right module ''M'' over a ''k''-algebra ''A'' is: :$\backslash operatorname\; =\; \backslash sup\_\; \backslash limsup\_\; \backslash log\_n\; \backslash dim\_k\; M\_0\; V^n$ where the sup is taken over all finite-dimensional subspaces $V\; \backslash subset\; A$ and $M\_0\; \backslash subset\; M$. An algebra is said to have polynomial growth if its Gelfand–Kirillov dimension is finite. == Basic facts == *The Gelfand–Kirillov dimension of a finitely generated commutative algebra ''A'' over a field is the Krull dimension of ''A'' (or equivalently the transcendence degree of the field of fractions of ''A'' over the base field.) *In particular, the GK dimension of the polynomial ring $k(\backslash dots,\; x\_n)$ Is ''n''. *(Warfield) For any real number ''r ''≥ 2, there exists a finitely generated algebra whose GK dimension is ''r''. 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「Gelfand–Kirillov dimension」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.