Displaying similar documents to “A characterization of p-bases of rings of constants”

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.

Positive characteristic analogs of closed polynomials

Piotr Jędrzejewicz (2011)

Open Mathematics

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The notion of a closed polynomial over a field of zero characteristic was introduced by Nowicki and Nagata. In this paper we discuss possible ways to define an analog of this notion over fields of positive characteristic. We are mostly interested in conditions of maximality of the algebra generated by a polynomial in a respective family of rings. We also present a modification of the condition of integral closure and discuss a condition involving partial derivatives.

The constants of the Volterra derivation

Pál Hegedűs (2012)

Open Mathematics

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The ring of constants of the Volterra derivation is found. Confirming a conjecture of Zielinski, it is always a polynomial ring.