Singular compactness and definability for Σ-cotorsion and Gorenstein modules

• Jan Šaroch ^[1] ; Jan Štovícek
  1. [1] Charles University in Prague

     Charles University in Prague

     Chequia

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 2, 2020
• Idioma: inglés
• DOI: 10.1007/s00029-020-0543-2
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• Resumen

  • 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.