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 unique factorization domain of characteristic p > 0. One of these conditions involves Jacobians while the other some properties of factors. In the case m = n this extends the known theorem of Nousiainen, and we obtain a new formulation of the Jacobian conjecture in positive characteristic.
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Jędrzejewicz, P. A characterization of p-bases of rings of constants. centr.eur.j.math. 11, 900–909 (2013). https://doi.org/10.2478/s11533-013-0207-y
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DOI: https://doi.org/10.2478/s11533-013-0207-y