Kähler differentials and differential algebra in arbitrary characteristic

Abstract:

Let L and K be differential fields with L an extension of K. It is shown how the module of Kähler differentials $\Omega _{L/K}^1$ can be used to “linearize” properties of a differential field extension $L/K$. This is done without restriction on the characteristic p and yields a theory which for $p \ne 0$ is no harder than the case $p = 0$. As an application a new proof of the Ritt basis theorem is given.