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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.

MSC:
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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