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

Bulletin of the Polish Academy of Sciences. Mathematics (2011)

- Volume: 59, Issue: 1, page 19-26
- ISSN: 0239-7269

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topPiotr 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 -

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