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arXiv · 2601.21466

A note on irreducible slice algebraic sets

Anna Gori·Giulia Sarfatti·Fabio Vlacci
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Abstract

In this short note we prove that if $I$ is a right radical and quasi prime ideal in the ring of quaternionic slice regular polynomials, then the symmetrization $\mathbb S_{V_c(I)}$ is an irreducible algebraic set, where $V_c(I)$ is the set of common zeros with commuting components of polynomials in $I$. Combining this fact with the results proved in our previous paper [3], we obtain that for $I$ radical, $V_c(I)$ is irreducible if and only if $I$ is quasi prime.

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Anna Gori, Giulia Sarfatti, Fabio Vlacci. 2026-05-19. A note on irreducible slice algebraic sets. https://arxiv.org/abs/2601.21466

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