Explicit minimal generating sets of a family of prime ideals with unbounded minimal number of generators in a three-dimensional power series ring
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910093562347520 |
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| author | González, Laura Planas-Vilanova, Francesc |
| author_facet | González, Laura Planas-Vilanova, Francesc |
| contents | We display a new family of prime ideals with unbounded minimal number of generators in a three-dimensional power series ring over a field of characteristic zero. These primes are obtained as the kernel of a quasi-monomial algebra homomorphism. Up to constant coefficients, determined by some specific linear systems with binomial entries, we describe their minimal generating polynomial sets. The advantage of our family with respect to some previous work is, on the one hand, the explicit description of the generating sets and, on the other hand, the simplicity of the exponents of the aforementioned quasi-monomial homomorphism. We also provide a code in Python which states and solves the linear systems that lead to a complete description of the minimal generating sets with a "Gröbner-free" approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00638 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Explicit minimal generating sets of a family of prime ideals with unbounded minimal number of generators in a three-dimensional power series ring González, Laura Planas-Vilanova, Francesc Commutative Algebra 13E15, 13H05, 13J05, 13P10, 14H50 We display a new family of prime ideals with unbounded minimal number of generators in a three-dimensional power series ring over a field of characteristic zero. These primes are obtained as the kernel of a quasi-monomial algebra homomorphism. Up to constant coefficients, determined by some specific linear systems with binomial entries, we describe their minimal generating polynomial sets. The advantage of our family with respect to some previous work is, on the one hand, the explicit description of the generating sets and, on the other hand, the simplicity of the exponents of the aforementioned quasi-monomial homomorphism. We also provide a code in Python which states and solves the linear systems that lead to a complete description of the minimal generating sets with a "Gröbner-free" approach. |
| title | Explicit minimal generating sets of a family of prime ideals with unbounded minimal number of generators in a three-dimensional power series ring |
| topic | Commutative Algebra 13E15, 13H05, 13J05, 13P10, 14H50 |
| url | https://arxiv.org/abs/2604.00638 |