Displaying similar documents to “Positive characteristic analogs of closed polynomials”

Irreducible Jacobian derivations in positive characteristic

Piotr Jędrzejewicz (2014)

Open Mathematics

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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.

A characterization of p-bases of rings of constants

Piotr Jędrzejewicz (2013)

Open Mathematics

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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.

Special isomorphisms of F [ x 1 , ... , x n ] preserving GCD and their use

Ladislav Skula (2009)

Czechoslovak Mathematical Journal

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On the ring R = F [ x 1 , ⋯ , x n ] of polynomials in n variables over a field F special isomorphisms A ’s of R into R are defined which preserve the greatest common divisor of two polynomials. The ring R is extended to the ring S = F [ [ x 1 , ⋯ , x n ] ] + and the ring T = F [ [ x 1 , ⋯ , x n ] ] of generalized polynomials in such a way that the exponents of the variables are non-negative rational numbers and rational numbers, respectively. The isomorphisms A ’s are extended to automorphisms B ’s of the ring S . Using the property that the isomorphisms A ’s preserve...