A characterization of p-bases of rings of constants

Abstract

We obtain two equivalent conditions for m polynomials in n variables to form a p-basis of a ring of constants of some polynomial K-derivation, where K is a UFD of characteristic p>0. One of these conditions involves jacobians, and the second - some properties of factors. In the case of m=n this extends the known theorem of Nousiainen, and we obtain a new formulation of the jacobian conjecture in positive characteristic.