On finitely injective modules and locally pure-injective modules over Pruefer domains

Over Matlis valuation domains there exist finitely injective modules which are not direct sums of injective modules, as well as complete locally pure-injective modules which are not the completion of a direct sum of pure-injective modules. Over Pruefer domains which are either almost maximal, or h-local Matlis, finitely injective torsion modules and complete torsionfree locally pure-injective modules correspond to each others under the Matlis equivalence. Almost maximal Pruefer domains are characterized by the property that every torsionfree complete module is locally pure-injective. It is derived that semi-Dedekind domains are Dedekind.