PUB - Publikationen an der Universität Bielefeld

Let R be a ring. An R-module M is called a Prüfer module provided there exists a locally nilpotent, surjective endomorphism of M with kernel of finite length. We want to outline the relevance, but also the ubiquity of Prüfer modules. The main assertion will be that any Prüfer module which is not of finite type gives rise to a generic module,thus to infinite families of indecomposable modules with fixed endo-length (here we are in the setting of the second Brauer-Thrall conjecture). In addition, we will report on a construction procedure which yields a wealth of Prüfer modules. Unfortunately, we do not know which modules obtained in this way are of finite type.