On weakly semisimple derivations of the polynomial ring in two variables

• Date: 2018
• Main Authors: Gavran, Volodimir, Stepukh, Vitaliy
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: polynomial ring; irreducible polynomial; Jacobian derivation; 13N15; 13N99
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1046
• Journal Title: Algebra and Discrete Mathematics

Let \(\mathbb K\) be an algebraically closed field of characteristic zero and \(\mathbb K[x,y]\) the polynomial ring. Every element \(f\in \mathbb K[x,y]\) determines the Jacobian derivation \(D_f\) of \(\mathbb K[x,y]\) by the rule D_f(h) = det J(f,h), where J(f,h) is the Jacobian matrix of the pol...