Dimension of complexes related to special Gorenstein projective precovers(II). Issue 3 (4th March 2023) - Liu, Zhongkui; Pengju, Ma
Abstract: Let R be a ring and X a complex of R -modules. We give some characterizations of the dimension of X related to special Gorenstein projective precovers. Let R be a ring such that ( G P, G P ⊥ ) forms a cotorsion pair cogenerated by a set, where G P denotes the category consisting of all Gorenstein projective R -modules. Then the dimension related to special Gorenstein projective precovers Gppd ( X ) is equal to the infimum of the set n ∈ Z | there exists a complete Gorenstein projective resolution of X T → σ G → X such that σi is bijective for each i ≥ n . Forthmore, if Gppd ( X ) is finite and n an integer then Gppd ( X ) ≤ n if and only if Ext G P i ( X, Q ) = 0 for any i > n and any projective R -module Q, where Ext G P i ( −, − ) is the relative cohomology functor.