Summary. Let K be a unique factorization domain of characteristic p > 0, and let f ∈ K[x_1,..., x_n] be a polynomial not lying in K[x_1~p,...,x_n~p]. We prove that K[x_1~p,..., x_n~p,f] is the ring of constants of a K-derivation of K[x_1,...,x_n] 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.
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