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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 thatforms a cotorsion pair cogenerated by a set, wheredenotes the category consisting of all Gorenstein projective  R -modules. Then the dimension related to special Gorenstein projective precoversis equal to the infimum of the setthere exists a complete Gorenstein projective resolution of  Xsuch that  σ iis bijective for eachForthmore, ifis finite and  n  an integer thenif and only iffor any  i  &gt;  n  and any projective  R -module  Q , whereis the relative cohomology functor.

Dimension of complexes related to special Gorenstein projective precovers(II)