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arXiv · 1511.04570

A short proof of Cartan's Nullstellensatz for entire functions in $\mathbb C^n$

Raymond Mortini
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Abstract

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 B\'ezout 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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Raymond Mortini. 2015-11-14. A short proof of Cartan's Nullstellensatz for entire functions in $\mathbb C^n$. https://doi.org/10.1007/s00013-015-0786-x

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