Zero sets and Nullstellensatz type theorems for slice regular quaternionic polynomials

TL;DR

This paper investigates the zero sets of slice regular quaternionic polynomials, providing a geometric characterization in two variables and establishing a quaternionic version of the Strong Hilbert Nullstellensatz.

Contribution

It introduces a geometric description of vanishing sets for slice regular polynomials and proves a new Nullstellensatz in the quaternionic context.

Findings

Geometric description of zero sets in two quaternionic variables

A new version of the Strong Hilbert Nullstellensatz for quaternions

Extension of classical polynomial root theorems to quaternionic polynomials

Abstract

We study the vanishing sets of slice regular polynomials in several quaternionic variables. We obtain a geometric description of the vanishing sets in two variables, which leads to a new version of the Strong Hilbert Nullstellensatz in the quaternionic setting.