A Characterization of One-Element p-Bases of Rings of Constants

• Autorzy: Piotr Jędrzejewicz
• Języki publikacji: EN

Abstrakty

EN

Let K be a unique factorization domain of characteristic p > 0, and let f ∈ K[x₁,...,xₙ] be a polynomial not lying in $K[x₁^p,...,xₙ^p]$. We prove that $K[x₁^p,...,xₙ^p,f]$ is the ring of constants of a K-derivation of K[x₁,...,xₙ] if and only if all the partial derivatives of f are relatively prime. The proof is based on a generalization of Freudenburg's lemma to the case of polynomials over a unique factorization domain of arbitrary characteristic.

Kategorie tematyczne

• 12E05: Polynomials (irreducibility, etc.)
• 13N15: Derivations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2011
• Tom: 59
• Numer: 1
• Strony: 19-26

Daty

wydano

2011

Twórcy

autor

Piotr Jędrzejewicz

• Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, 87-100 Toruń, Poland

Identyfikatory

DOI

10.4064/ba59-1-3