$VW$-Gorenstein complexes

Abstract

Let V, W be two classes of modules. In this paper, we introduce and study VW -Gorenstein complexes as a common generalization of W -complexes, Gorenstein projective (resp., Gorenstein injective) complexes, and GCprojective (resp., GC -injective) complexes. It is shown that under certain hypotheses a complex X is VW -Gorenstein if and only if each X n is a VW -Gorenstein module. This result unifies the corresponding results of the aforementioned complexes. As an application, the stability of VW -Gorenstein complexes is explored.