Variable lemma for polynomial rings
Let \(k\) be a field of characteristic zero, and let \(k[x_1,\ldots,x_n]\) be a polynomial ring in \(n\) variables, where \(n\geq 3\) is an arbitrary positive integer. Assume that we have \(l\in\mathbb{N}\) algebraically independent polynomials \(F_1,\ldots,F_l\in k[x_1,\ldots,x_n]\) with \(2\leq l...
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| Datum: | 2026 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2026
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| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2428 |
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| Назва журналу: | Algebra and Discrete Mathematics |
| Завантажити файл: |  |
Institution
Algebra and Discrete Mathematics| Zusammenfassung: | Let \(k\) be a field of characteristic zero, and let \(k[x_1,\ldots,x_n]\) be a polynomial ring in \(n\) variables, where \(n\geq 3\) is an arbitrary positive integer. Assume that we have \(l\in\mathbb{N}\) algebraically independent polynomials \(F_1,\ldots,F_l\in k[x_1,\ldots,x_n]\) with \(2\leq l <n.\) In this paper, we prove that if linear parts of polynomials \(F_1,\ldots,F_l\) are linearly independent and depend only on variables \(x_1,\ldots,x_l\) and the polynomials \(F_1,\ldots,F_l\) meet some weighted-differential criteria then actually \(F_1,\ldots,F_l\in k[x_1,\ldots,x_l].\) |
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| DOI: | 10.12958/adm2428 |