Abstract
Let R be a ring and 𝒲 a self-orthogonal class of left R-modules which is closed under finite direct sums and direct summands. A complex C of left R-modules is called a 𝒲-complex if it is exact with each cycle Z n (C) ∈ 𝒲. The class of such complexes is denoted by 𝒞𝒲. A complex C is called completely 𝒲-resolved if there exists an exact sequence of complexes D · = … → D −1 → D 0 → D 1 → … with each term D i in 𝒞𝒲 such that C = ker(D 0 → D 1) and D · is both Hom(𝒞𝒲, −) and Hom(−, 𝒞𝒲) exact. In this article, we show that C = … → C −1 → C 0 → C 1 → … is a completely 𝒲-resolved complex if and only if C n is a completely 𝒲-resolved module for all n ∈ ℤ. Some known results are obtained as corollaries.
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