Closed polynomials and saturated subalgebras of polynomial algebras

• Date: 2007
• Main Authors: Arzhantsev, I. V., Petravchuk, A. P., Аржанцев, І.В., Петравчук, А. П.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2007
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3414
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

The behavior of closed polynomials, i.e., polynomials $f ∈ k[x_1,…,x_n]∖k$ such that the subalgebra $k[f]$ is integrally closed in $k[x_1,…,x_n]$, is studied under extensions of the ground field. Using some properties of closed polynomials, we prove that, after shifting by constants, every polynomia...