On closed rational functions in several variables

• Date: 2018
• Main Authors: Petravchuk, Anatoliy P., Iena, Oleksandr G.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: closed rational functions; irreducible polynomials; 26C15
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/848
• Journal Title: Algebra and Discrete Mathematics

Let \(\mathbb K= \bar{\mathbb K}\) be a field of characteristic zero. An element \(\varphi\in \mathbb K(x_1,\dots, x_{n})\) is called a closed rational function if the subfield \(\mathbb K(\varphi)\) is algebraically closed in the field \(\mathbb K(x_1,\dots, x_{n})\). We prove that a rational funct...