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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2507.21674 |
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| _version_ | 1866909787978989568 |
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| author | Gori, Anna Sarfatti, Giulia Vlacci, Fabio |
| author_facet | Gori, Anna Sarfatti, Giulia Vlacci, Fabio |
| contents | In the present paper we investigate the relations between irreducible slice algebraic sets in $\mathbb{H}^n$ and quasi prime right ideals of the ring of slice regular polynomials in $n$ quaternionic variables. We provide algebraic conditions on right ideals of slice regular polynomials which guarantee the irreducibility of the corresponding slice algebraic sets and show that radical ideals associated with irreducible slice algebraic sets are quasi prime. Furthermore we establish that this correspondence is an equivalence in the case of principal right ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_21674 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the irreducibility of slice algebraic sets Gori, Anna Sarfatti, Giulia Vlacci, Fabio Algebraic Geometry 30G35, 16S36 In the present paper we investigate the relations between irreducible slice algebraic sets in $\mathbb{H}^n$ and quasi prime right ideals of the ring of slice regular polynomials in $n$ quaternionic variables. We provide algebraic conditions on right ideals of slice regular polynomials which guarantee the irreducibility of the corresponding slice algebraic sets and show that radical ideals associated with irreducible slice algebraic sets are quasi prime. Furthermore we establish that this correspondence is an equivalence in the case of principal right ideals. |
| title | On the irreducibility of slice algebraic sets |
| topic | Algebraic Geometry 30G35, 16S36 |
| url | https://arxiv.org/abs/2507.21674 |