Universally Finite Differential Algebras

Abstract

In previous sections we have seen how differential algebras and differential modules can be used to define invariants of algebras and prove structure theorems about them. Frequently it was necessary to impose finiteness conditions on the differential modules under consideration. But already for a simple ring like the power series ring R over a field K of characteristic O the differential module $\Omega _{R/K}^1$ is not finitely generated (5.5a)). Fortunately, a mo-dification of $\Omega _{R/K}^1$, the “universally finite” differential module, which we will discuss here and in the following sections, allso to handle such rings like affine algebras.