TY - JOUR
AU - I. V. Arzhantsev
AU - A. P. Petravchuk
PY - 2007/12/25
Y2 - 2023/03/26
TI - Closed polynomials and saturated subalgebras of polynomial algebras
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 59
IS - 12
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/3414
AB - 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 $A$.
ER -