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

2024/02/26 by Gori, Anna, Sarfatti, Giulia, Vlacci, Fabio · 1 citation
#15A54 #16S36 #30G35 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2402.16784

Abstract

In this paper we prove a strong version of the Hilbert Nullstellensatz in the ring \mathbb H[q₁,…,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[q₁,…,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 Hⁿ.

Cited by

• On the irreducibility of slice algebraic sets

Related

• Zero sets and Nullstellensatz type theorems for slice regular quaternionic polynomials
• Ideals of regular functions of a quaternionic variable
• Resultants of slice regular polynomials in two quaternionic variables
• A Quaternionic Nullstellensatz
• Hilbert's Nullstellensatz over quaternions