Singular compactness and definability for Σ-cotorsion and Gorenstein modules

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 module...

Full description

Saved in:
Bibliographic Details
Published in:Selecta mathematica (Basel, Switzerland) Switzerland), 2020-05, Vol.26 (2), Article 23
Main Authors: Šaroch, Jan, Št’ovíček, Jan
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Modules
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1022-1824
1420-9020
DOI:10.1007/s00029-020-0543-2