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