Resumen de Singular compactness and definability for Σ-cotorsion and Gorenstein modules

Jan Šaroch, Jan Štovícek

• We introduce a general version of the singular compactness theorem which makes it possible to show that being a Σ-cotorsion module is a property of the complete theory of the module. As an application of the powerful tools developed along the way, we give a new description of Gorenstein flat modules which implies that, regardless of the ring, the class of all Gorenstein flat modules forms the left-hand class of a perfect cotorsion pair. We also prove the dual result for Gorenstein injective modules.