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arXiv · 1804.09080

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

Jan Šaroch·Jan Šťovíček
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Abstract

We introduce a general version of 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.

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Jan Šaroch, Jan Šťovíček. 2018-04-24. Singular compactness and definability for $\Sigma$-cotorsion and Gorenstein modules. https://doi.org/10.1007/s00029-020-0543-2

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