Singular compactness and definability for $\Sigma$-cotorsion and Gorenstein modules
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2018
- DOI:
- 10.48550/arXiv.1804.09080
- arXiv:
- arXiv:1804.09080
- Bibcode:
- 2018arXiv180409080S
- Keywords:
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- Mathematics - Representation Theory;
- Mathematics - Logic;
- Mathematics - Rings and Algebras;
- 16E30 (primary);
- 16B70;
- 03E75 (secondary)
- E-Print:
- 34 pages