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.

Anexos:

• yves.pdf