On some regularity condition

被引:0
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作者
Beata Gryszka
Janusz Gwoździewicz
机构
[1] Pedagogical University of Cracow,Institute of Mathematics
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Regular function; Rational representation; Bertini’s theorem; Hensel’s lemma;
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摘要
Let K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {K}$$\end{document} be an uncountable field of characteristic zero and let f be a function from Kn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {K}^n$$\end{document} to K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {K}$$\end{document}. We show that if the restriction of f to every affine plane L⊂Kn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L\subset \mathbb {K}^n$$\end{document} is regular, then f is a regular function.
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页码:336 / 342
页数:6
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