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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.01378 |
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| _version_ | 1866909090900344832 |
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| author | Alon, Gil Paran, Elad |
| author_facet | Alon, Gil Paran, Elad |
| contents | Let R be the ring of polynomials in n central variables over the real quaternion algebra H, and let I be a left ideal in R. We prove that if a polynomial p in R vanishes at all the common zeros of I in H^n with commuting coordinates, then as a slice regular quaternionic function, p vanishes at all common zeros of I in H^n. This confirms a conjecture of Gori, Sarfatti and Vlacci, who settled the two dimensional case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01378 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the geometry of zero sets of central quaternionic polynomials Alon, Gil Paran, Elad Rings and Algebras Algebraic Geometry Let R be the ring of polynomials in n central variables over the real quaternion algebra H, and let I be a left ideal in R. We prove that if a polynomial p in R vanishes at all the common zeros of I in H^n with commuting coordinates, then as a slice regular quaternionic function, p vanishes at all common zeros of I in H^n. This confirms a conjecture of Gori, Sarfatti and Vlacci, who settled the two dimensional case. |
| title | On the geometry of zero sets of central quaternionic polynomials |
| topic | Rings and Algebras Algebraic Geometry |
| url | https://arxiv.org/abs/2402.01378 |