zbMATH — the first resource for mathematics

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:
 1.6e+31 Homological functors on modules (Tor, Ext, etc.) in associative algebras 1.6e+66 Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)
Full Text:
References:
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.