Turkish Journal of Mathematics
Abstract
Let $\A$ be an abelian category, and $\V$,$\W$ two additive full subcategories of $\A$. We introduce and study the $\V\W$-Gorenstein subcategory of $\A$, which unifies many known notions, such as the Gorenstein category and the category consisting of $G_C$-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 $\V\W$-Gorenstein category. The connections between $\V\W$-Gorenstein categories and Gorenstein categories are discussed. Some applications are given.
DOI
10.3906/mat-1502-37
Keywords
($\V$$\W$-)Gorenstein categories, semidualizing modules, Gorenstein projective modules, Gorenstein injective modules, Bass class
First Page
365
Last Page
375
Recommended Citation
ZHAO, G, & SUN, J (2016). $\V\W$-Gorenstein categories. Turkish Journal of Mathematics 40 (2): 365-375. https://doi.org/10.3906/mat-1502-37
