The Combinatorial Nullstellensatz, Chevalley-Warning Theorem and weak Finitesatz in skew polynomial rings
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916897820246016 |
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| author | Alon, Gil Behajaina, Angelot Paran, Elad |
| author_facet | Alon, Gil Behajaina, Angelot Paran, Elad |
| contents | We study zeros of polynomials in the multivariate skew polynomial ring $D[x_1,\ldots,x_n; σ]$, where $σ$ is an automorphism of a division ring $D$. We prove a generalization of Alon's celebrated Combinatorial Nullstellensatz for such polynomials. In the case where $D$ is a finite field, we prove skew analogues of the Chevalley--Warning theorem, Ax's Lemma, and the weak case of Terjanian's Finitesatz. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07257 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Combinatorial Nullstellensatz, Chevalley-Warning Theorem and weak Finitesatz in skew polynomial rings Alon, Gil Behajaina, Angelot Paran, Elad Commutative Algebra Combinatorics Rings and Algebras We study zeros of polynomials in the multivariate skew polynomial ring $D[x_1,\ldots,x_n; σ]$, where $σ$ is an automorphism of a division ring $D$. We prove a generalization of Alon's celebrated Combinatorial Nullstellensatz for such polynomials. In the case where $D$ is a finite field, we prove skew analogues of the Chevalley--Warning theorem, Ax's Lemma, and the weak case of Terjanian's Finitesatz. |
| title | The Combinatorial Nullstellensatz, Chevalley-Warning Theorem and weak Finitesatz in skew polynomial rings |
| topic | Commutative Algebra Combinatorics Rings and Algebras |
| url | https://arxiv.org/abs/2508.07257 |