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Foxby equivalences of Cartan-Eilenberg complexes. (English) Zbl 1449.16016

Summary: Let \(R\) be a commutative Noetherian ring with a semi-dualizing module \(C\). We introduce CE (abbreviation for Cartan-Eilenberg) Auslander class CE-\({\mathcal{A}_c} (R)\) and CE Bass class CE-\({\mathcal{B}_c} (R)\), and extend the Foxby equivalence to the setting of CE complexes.

MSC:

16D90 Module categories in associative algebras
16E05 Syzygies, resolutions, complexes in associative algebras
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