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

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 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.