Non-free iterative differential modules

Abstract

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.

11 pages. arXiv admin note: text overlap with arXiv:1304.7663

References in corpus (2)

• The inverse problem of differential Galois theory over the field R(z)
• Picard-Vessiot theory of differentially simple rings