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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 Algebraic function field ： ウィキペディア英語版 Algebraic function field In mathematics, an (algebraic) function field of ''n'' variables over the field ''k'' is a finitely generated field extension ''K''/''k'' which has transcendence degree ''n'' over ''k''. Equivalently, an algebraic function field of ''n'' variables over ''k'' may be defined as a finite field extension of the field ''k''(''x''1,...,''x''''n'') of rational functions in ''n'' variables over ''k''. ==Example== As an example, in the polynomial ring ''k''() consider the ideal generated by the irreducible polynomial ''Y''2−''X''3 and form the field of fractions of the quotient ring ''k''()/(''Y''2−''X''3). This is a function field of one variable over ''k''; it can also be written as $k(X)(\backslash sqrt)$ (with degree 2 over $k(X)$) or as $k(Y)(\backslash sqrt())$ (with degree 3 over $k(Y)$). We see that the degree of an algebraic function field is not a well-defined notion. 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「Algebraic function field」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.