  In the article "Picard-Vessiot theory of differentially simple rings" we
established a Picard-Vessiot theory over differentially simple rings which may
not be fields. Differential modules over such rings were proven to be locally
free but do not have to be free as modules. In this article, we give a family
of examples of non-free differential modules, and compute Picard-Vessiot rings
as well as Galois groups for them.
