Closed polynomials and saturated subalgebras of polynomial algebras

• Published in: Український математичний журнал
• Date: 2007
• ISSN: 1027-3190
• Main Authors: Arzhantsev, I.V., Petravchuk, A.P.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2007
• Subjects: Статті
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/172514
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Closed polynomials and saturated subalgebras of polynomial algebras / I.V. Arzhantsev, A.P. 
 Petravchuk // Український математичний журнал. — 2007. — Т. 59, № 12. — С. 1587–1593. — Бібліогр.: 15 назв. — англ.

The behavior of closed polynomials, i.e., polynomials f∈k[x₁,…,xn]∖k such that the subalgebra k[f] is integrally closed in k[x₁,…,xn], is studied under extensions of the ground field. Using some properties of closed polynomials, we prove that, after shifting by constants, every polynomial f∈k[x₁,…,x...