A short proof of Cartan’s Nullstellensatz for entire functions in Cn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{C}^n}$$\end{document}

被引:0
|
作者
Raymond Mortini
机构
[1] Université de Lorraine,Département de Mathématiques et Institut Élie Cartan de Lorraine, UMR 7502
关键词
Entire functions; Cartan’s Nullstellensatz; Polydisk algebra; Maximal ideals; Primary 32A15; Secondary 46J15;
D O I
10.1007/s00013-015-0786-x
中图分类号
学科分类号
摘要
Using the fact that the maximal ideals in the polydisk algebra are given by the kernels of point evaluations, we derive a simple formula that gives a solution to the Bézout equation in the space of all entire functions of several complex variables. Thus a short and easy analytic proof of Cartan’s Nullstellensatz is obtained.
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页码:149 / 152
页数:3
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