Variable lemma for polynomial rings

• Date: 2026
• Main Authors: Holik, Daria, Karaś, Marek
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2026
• Subjects: polynomial automorphism; tame (wild) automorphism; (weighted) multidegree; general algebraic group; Primary: 13N05; 14R10. Secondary: 13B25; 13N15; 14L40
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2428
• Journal Title: Algebra and Discrete Mathematics

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...