Closed polynomials and saturated subalgebras of polynomial algebras

  • I. V. Arzhantsev
  • A. P. Petravchuk Kyiv Nat. Taras Shevchenko Univ., Ukraine


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 polynomial $f ∈ k[x_1,…,x_n]∖k$ can be factorized into a product of irreducible polynomials of the same degree. We consider some types of saturated subalgebras $A ⊂ k[x_1,…,x_n]$, i.e., subalgebras such that, for any $f ∈ A∖k$, a generative polynomial of $f$ is contained in $A$.
How to Cite
Arzhantsev, I. V., and A. P. Petravchuk. “Closed Polynomials and Saturated Subalgebras of Polynomial Algebras”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, no. 12, Dec. 2007, pp. 1587–1593,
Research articles