Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: Ring of constants

Sortuj według:

Ogranicz wyniki do:

Positive characteristic analogs of closed polynomials

100%

Jędrzejewicz P.

Open Mathematics

2011

tom 9

nr 1

50-56

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.

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

3 Open Mathematics

3 Jędrzejewicz P.

1 2014

1 2013

1 2011

Wyniki wyszukiwania

Positive characteristic analogs of closed polynomials

A characterization of p-bases of rings of constants

Irreducible Jacobian derivations in positive characteristic