ABSTRACT
Let π²,π΄,π³ be three classes of left R-modules. In this paper, we introduce and study (π²,π΄,π³)-Gorenstein complexes as a common generalization of completely π²-resolved complexes [Citation26], Gorenstein projective (resp., injective) complexes [Citation8], Ding projective (resp., injective) complexes [Citation32] and Gorenstein AC-projective (resp., AC-injective) complexes [Citation4]. It is shown that under certain hypotheses, a complex C is (π²,π΄,π³)-Gorenstein if and only if each Cn is a (π²,π΄,π³)-Gorenstein module and are exact for any
. This result unifies the corresponding results of the aforementioned complexes. As applications, the stability of (π²,π΄,π³)-Gorenstein complexes and modules are explored.
Acknowledgments
The authors are grateful to the anonymous referee for the careful reading of this article and many useful suggestions. This research was partially supported by the National Natural Science Foundation of China (11371187, 11361051, 11361052).