Abstract
ABSTRACTLet 𝒲,𝒴,𝒳 be three classes of left R-modules. In this paper, we introduce and study (𝒲,𝒴,𝒳)-Gorenstein complexes as a common generalization of completely 𝒲-resolved complexes [26], Gorenstein projective (resp., injective) complexes [8], Ding projective (resp., injective) complexes [32] and Gorenstein AC-projective (resp., AC-injective) complexes [4]. It is shown that under certain hypotheses, a complex C is (𝒲,𝒴,𝒳)-Gorenstein if and only if each Cn is a (𝒲,𝒴,𝒳)-Gorenstein module and are exact for any . This result unifies the corresponding results of the aforementioned complexes. As applications, the stability of (𝒲,𝒴,𝒳)-Gorenstein complexes and modules are explored.
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