Abstract
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.
Citation
Wanru Zhang. Zhongkui Liu. Xiaoyan Yang. "Foxby equivalences associated to strongly Gorenstein modules." Kodai Math. J. 41 (2) 397 - 412, June 2018. https://doi.org/10.2996/kmj/1530496849
