Displaying similar documents to “Derivations satisfying polynomial identities”

Local derivations in polynomial and power series rings

Janusz Zieliński (2002)

Colloquium Mathematicae


We give a description of all local derivations (in the Kadison sense) in the polynomial ring in one variable in characteristic two. Moreover, we describe all local derivations in the power series ring in one variable in any characteristic.

A characterization of p-bases of rings of constants

Piotr Jędrzejewicz (2013)

Open Mathematics


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.