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- W3083960725 abstract "Let R be a ring such that (GP,GP⊥) forms a cotorsion pair cogenerated by a set, where GP denotes the category of all Gorenstein projective R-modules. Recently, the first author defined for any complex X the relative cohomology functors ExtGP⁎(X,−) as H−⁎(Hom(G,−)) in which G is a special Gorenstein projective precover of X. In the present paper, we introduce the dimension of X related to Gorenstein projective precovers, and show that such a dimension of X is equal to the least integer n for which ExtGPi(X,Q)=0 for all i>n and all R-modules Q∈GP⊥. This result gives a “Gorenstein” version of the relationship between the projective dimension of complexes introduced by Avramov and Foxby and the absolutely cohomology functors ExtR⁎(−,−)." @default.
- W3083960725 created "2020-09-14" @default.
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- W3083960725 date "2021-01-01" @default.
- W3083960725 modified "2023-10-17" @default.
- W3083960725 title "Relative cohomology of complexes II: Vanishing of relative cohomology" @default.
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- W3083960725 doi "https://doi.org/10.1016/j.jalgebra.2020.08.020" @default.
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