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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 pseudo algebraically closed field ： ウィキペディア英語版 pseudo algebraically closed field In mathematics, a field $K$ is pseudo algebraically closed if it satisfies certain properties which hold for any algebraically closed field. The concept was introduced by James Ax in 1967.〔Fried & Jarden (2008) p.218〕 ==Formulation== A field ''K'' is pseudo algebraically closed (usually abbreviated by PAC〔) if one of the following equivalent conditions holds: *Each absolutely irreducible variety $V$ defined over $K$ has a $K$-rational point. *For each absolutely irreducible polynomial $f\backslash in\; K(,T\_r,X)$ with $\backslash frac\backslash not\; =0$ and for each nonzero $g\backslash in\; K(,T\_r)$ there exists $(\backslash textbf,b)\backslash in\; K^$ such that $f(\backslash textbf,b)=0$ and $g(\backslash textbf)\backslash not\; =0$. *Each absolutely irreducible polynomial $f\backslash in\; K()$ has infinitely many $K$-rational points. *If $R$ is a finitely generated integral domain over $K$ with quotient field which is regular over $K$, then there exist a homomorphism $h:R\backslash to\; K$ such that $h(a)=a$ for each $a\backslash in\; K$ 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「pseudo algebraically closed 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.