arXiv 1804.090802018-04math.RTmath.LOmath.RA

Singular compactness and definability for $Σ$-cotorsion and Gorenstein modules

Jan Šaroch, Jan Šťovíček

备注：: 34 pages; small changes made and details added
发表信息：: Sel. Math. New Ser. 26, 23 (2020)
DOI：: 10.1007/s00029-020-0543-2

英文摘要：

We introduce a general version of 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.

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