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Foxby equivalences associated to strongly Gorenstein modules. (English) Zbl 1441.16009
Summary: In order to establish the Foxby equivalences associated to strongly Gorenstein modules, we introduce the notions of strongly \(\mathcal{W}_P\)-Gorenstein, \(\mathcal{W}_I\)-Gorenstein and \(\mathcal{W}_F\)-Gorenstein modules and discuss some basic properties of these modules. We show that the subcategory of strongly Gorenstein projective left \(R\)-modules in the left Auslander class and the subcategory of strongly \(\mathcal{W}_P\)-Gorenstein left \(S\)-modules are equivalent under Foxby equivalence. The injective and flat case are also studied.

16E30 Homological functors on modules (Tor, Ext, etc.) in associative algebras
16E65 Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)
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