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arXiv · 2402.16784

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

Anna Gori·Giulia Sarfatti·Fabio Vlacci
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Abstract

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

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Anna Gori, Giulia Sarfatti, Fabio Vlacci. 2024-02-26. A Strong Version of the Hilbert Nullstellensatz for slice regular polynomials in several quaternionic variables. https://arxiv.org/abs/2402.16784

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