On closed rational functions in several variables

• Published in: Algebra and Discrete Mathematics
• Date: 2007
• Main Authors: Petravchuk, A.P., Iena, O.G.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2007
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/157399
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On closed rational functions in several variables / A.P. Petravchuk, O.G. Iena // Algebra and Discrete Mathematics. — 2007. — Vol. 6, № 2. — С. 115–124. — Бібліогр.: 10 назв. — англ.

Let K = K¯ be a field of characteristic zero. An element ϕ ∈ K(x1,... ,xn) is called a closed rational function if the subfield K(ϕ) is algebraically closed in the field K(x1,... ,xn). We prove that a rational function ϕ = f/g is closed if f and g are algebraically independent and at least one o...