Singular compactness and definability for $$\Sigma $$-cotorsion and Gorenstein modules

By Jan Saroch, J. Št’ovíček. 2018

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We introduce a general version of the singular compactness theorem which makes it possible to show that being a $$\Sigma $$-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.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/005b5550bfbbea081fe1cf233867e58bf9c407ff