Model theory of modules over a serial ring Original Research Article

We use the Drozd-Warfield structure theorem for finitely presented modules over a serial ring to investigate the model theory of modules over a serial ring, in particular, to give a simple description of pp-formulas and to classify the pure-injective indecomposable modules. We also study the question of whether every pure-injective indecomposable module over a valuation ring is the hull of a uniserial module.