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A characterization of p-bases of rings of constants

100%

Jędrzejewicz P.

Open Mathematics

2013

tom 11

nr 5

900-909

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.

Irreducible Jacobian derivations in positive characteristic

100%

Jędrzejewicz P.

Open Mathematics

2014

tom 12

nr 8

1278-1284

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.

Ograniczanie wyników

2 Open Mathematics

2 Jędrzejewicz P.

1 2014

1 2013

Wyniki wyszukiwania

A characterization of p-bases of rings of constants

Irreducible Jacobian derivations in positive characteristic