Quasi semiprime multiplication modules over a pullback of a pair of Dedekind domains

The main purpose of this article is to classify all indecomposable quasi semiprime multiplication modules over pullback rings of two Dedekind domains and establish a connection between the quasi semiprime multiplication modules and the pure-injective modules over such rings. First, we introduce and study the notion of quasi semiprime multiplication modules and classify quasi semiprime multiplication modules over local Dedekind domains. Second, we get all indecomposable separated quasi semiprime multiplication modules and then, using this list of separated quasi-semiprime multiplication modules, we show that non-separated indecomposable quasi semiprime multiplication R-modules with finite-dimensional top are factor modules of finite direct sums of separated indecomposable quasi semiprime multiplication modules.