Preprint A199/2003
Differential simplicity in polynomial rings and algebraic independence of power series

Daniel Levcovitz | Brumatti, Paulo | Lequain, Yves

**Keywords: **
differential simplicity | polynomials | algebraic independence | power series

Let k be a field of characteristic zero and d a derivation of
K[X,Y]. We establish a connection between the d-simplicity of the localization of K[X,Y] at (X,Y) and the transcendency of the solution in tk[[t]] of a certain algebraic differential equation. We use this connection to obtain some interestinng results in the theory of the formal power series and to construct new examples of differentially simple rings.