Closed polynomials and saturated subalgebras of polynomial algebras

Authors

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

Abstract

The behavior of closed polynomials, i.e., polynomials fk[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 fk[x1,,xn]k can be factorized into a product of irreducible polynomials of the same degree. We consider some types of saturated subalgebras Ak[x1,,xn], i.e., subalgebras such that, for any fAk, a generative polynomial of f is contained in A.

Published

25.12.2007

Issue

Section

Research articles

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, https://umj.imath.kiev.ua/index.php/umj/article/view/3414.