1. Gorenstein (ℒ,풜)-flat dimension of complexes and relative singularity categories.
- Author
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Chen, Wenjing
- Abstract
Assume that the class of all Gorenstein (ℒ,풜)-flat modules is closed under extensions. We define a notion of Gorenstein (ℒ,풜)-flat dimension for complexes and consider equivalent characterizations of the finiteness of Gorenstein (ℒ,풜)-flat dimension of complexes. Furthermore, in addition, assume that R is a right coherent ring. We construct the relative singularity category with respect to Gorenstein (ℒ,풜)-flat modules, as the triangulated quotient of the triangulated subcategory of Db(R) consisting of all complexes with both finite Gorenstein (ℒ,풜)-flat dimension and cotorsion dimension by the bounded homotopy category of flat-cotorsion modules, and show that the relative singularity category is triangulated equivalent to the stable category of the Frobenius category consisting of all Gorenstein (ℒ,풜)-flat and cotorsion modules. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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