Let K be a unique factorization domain of characteristic p > 0, and let f ∈ K[x₁,...,xₙ] be a polynomial not lying in . We prove that 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba59-1-3,
author = {Piotr J\k edrzejewicz},
title = {A Characterization of One-Element p-Bases of Rings of Constants},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {59},
year = {2011},
pages = {19-26},
zbl = {1216.13017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba59-1-3}
}
Piotr Jędrzejewicz. A Characterization of One-Element p-Bases of Rings of Constants. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 59 (2011) pp. 19-26. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba59-1-3/