부산대학교 도서관

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. [ABSTRACT FROM AUTHOR]