  Picard-Vessiot rings are present in many settings like differential Galois
theory, difference Galois theory and Galois theory of Artinian simple module
algebras. In this article we set up an abstract framework in which we can prove
theorems on existence and uniqueness of Picard-Vessiot rings, as well as on
Galois groups corresponding to the Picard-Vessiot rings. As the present
approach restricts to the categorical properties which all the categories of
differential modules resp. difference modules etc. share, it gives unified
proofs for all these Galois theories (and maybe more general ones).
