On divergence and sums of derivations

• Date: 2017
• Main Authors: Chapovsky, E., Shevchyk, O.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2017
• Subjects: polynomial ring; derivation; divergence; jacobian derivation; transcendence basis; Primary 13N15; Secondary 13A99; 17B66
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/354
• Journal Title: Algebra and Discrete Mathematics

Let \(K\) be an algebraically closed   field of characteristic zero and \(A\)  a field of algebraic functions in \(n\) variables over \(\mathbb K\). (i.e. \(A\) is a finite dimensional algebraic extension of the field \(\mathbb K(x_1, \ldots, x_n)\) ). If \(\textit{D}\) is a \(\mathbb K\)-derivation...