A note on irreducible slice algebraic sets
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911698014699520 |
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| author | Gori, Anna Sarfatti, Giulia Vlacci, Fabio |
| author_facet | Gori, Anna Sarfatti, Giulia Vlacci, Fabio |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_21466 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A note on irreducible slice algebraic sets Gori, Anna Sarfatti, Giulia Vlacci, Fabio Algebraic Geometry 30G35, 16S36 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. |
| title | A note on irreducible slice algebraic sets |
| topic | Algebraic Geometry 30G35, 16S36 |
| url | https://arxiv.org/abs/2601.21466 |