A Strong Version of the Hilbert Nullstellensatz for slice regular polynomials in several quaternionic variables

In this paper we prove a strong version of the Hilbert Nullstellensatz in thering $\mathbb H[q_1,\ldots,q_n]$ of slice regular polynomials in severalquaternionic variables. Our proof deeply depends on a detailed analysis of thecommon zeros of slice regular polynomials which belong to an ideal in $\mathbbH[q_1,\ldots,q_n]$. This study motivates the introduction of a new notion ofalgebraic set in the quaternionic setting, which allows us to define aZariski-type topology on $\mathbb H^n$.