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

Piotr Jędrzejewicz. "A Characterization of One-Element p-Bases of Rings of Constants." Bulletin of the Polish Academy of Sciences. Mathematics 59.1 (2011): 19-26. <http://eudml.org/doc/281292>.

@article{PiotrJędrzejewicz2011,
abstract = {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.},
author = {Piotr Jędrzejewicz},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {derivations; rings of constants; -bases},
language = {eng},
number = {1},
pages = {19-26},
title = {A Characterization of One-Element p-Bases of Rings of Constants},
url = {http://eudml.org/doc/281292},
volume = {59},
year = {2011},
}

TY - JOUR
AU - Piotr Jędrzejewicz
TI - A Characterization of One-Element p-Bases of Rings of Constants
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2011
VL - 59
IS - 1
SP - 19
EP - 26
AB - 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.
LA - eng
KW - derivations; rings of constants; -bases
UR - http://eudml.org/doc/281292
ER -