Marcos Mazari Armida, Carnegie Mellon University

Title: Torsion modules with pure embeddings

Abstract: We study Martsinkovsky-Russell torsion modules with pure embeddings as an abstract elementary class (AEC for short). We show that the class is stable (in the AEC sense). Using that the class of torsion abelian groups is stable, we will present a solution to a problem of László Fuchs. We characterize when the class is superstable (in the AEC sense).  In order to fulfill this goal, we develop relative notions of pure-injectivity and $\Sigma$-pure-injectivity. We will not assume any familiarity with abstract elementary classes and we will introduce all the basic notions.