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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 Lüroth's theorem ： ウィキペディア英語版 Lüroth's theorem In mathematics, Lüroth's theorem asserts that every field that lies between two other fields ''K'' and ''K''(''X'') must be generated as an extension of ''K'' by a single element of ''K''(''X''). This result is named after Jacob Lüroth, who proved it in 1876. ==Statement== Let $K$ be a field and $M$ be an intermediate field between $K$ and $K(X)$, for some indeterminate ''X''. Then there exists a rational function $f(X)\backslash in\; K(X)$ such that $M=K(f(X))$. In other words, every intermediate extension between $K$ and $K(X)$ is a simple extension. 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「Lüroth'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.