Irreducible Jacobian derivations in positive characteristic

Piotr Jędrzejewicz 1
  • 1 Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100, Toruń, Poland

Abstract

We prove that an irreducible polynomial derivation in positive characteristic is a Jacobian derivation if and only if there exists an (n-1)-element p-basis of its ring of constants. In the case of two variables we characterize these derivations in terms of their divergence and some nontrivial constants.

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