In this paper, we study the relation between m-strongly Gorenstein projective (resp. injective) modules and n-strongly Gorenstein projective (resp. injective) modules whenever m = n, and the homological behavior of n-strongly Gorenstein projective (resp. injective) modules. We introduce the notion of n-strongly Gorenstein flat modules. Then we study the homological behavior of n-strongly Gorenstein flat modules, and the relation between these modules and n-strongly Gorenstein projective (resp. injective)
Let A be an abelian category, and V , W two additive full subcategories of A . We introduce and study the VW -Gorenstein subcategory of A , which unifies many known notions, such as the Gorenstein category and the category consisting of GC -projective (injective) modules, although they were defined in a different way. We also prove that the Bass class with respect to a semidualizing module is one kind of VW -Gorenstein category. The connections between VW -Gorenstein categories and Gorenstein categories are discussed. Some applications are given.
In this paper, we first investigate the relationship between W-(co)resolutions and X -(co)resolutions for two full subcategories W and X of an abelian category with W ⊆ X . Then some applications are given. In particular, we obtain the stability of the category of C-Gorenstein flat modules under the procedure used to define these entities, which is different from that established by Sather-Wagstaff, Sharif and White. 2010 AMS Mathematics subject classification. Primary 16E05, 16E30, 18G10. Keywords and phrases. X -(co)resolution, (co)generator, semidualizing module, Gorenstein flat module, stability of category.
As the dual of the Auslander transpose and the resulting k-torsionfree module, the cotranspose and k-cotorsionfree module with respect to a semidualizing bimodule have been introduced recently. In this paper we first investigate the relation between relative k-cotorsionfree modules and relative k-cosyzygy modules. Then we study the extension closure of these two classes of modules.
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