| In this paper,two classes of complexes are discussed,which are called FCprojective complexes and Gorenstein FC-projective complexes respectively.Some homological properties of these classes are investigated.Firstly,we give the structural characterization of the FC-projective complexes,and prove that a complex C is FCprojective complexes if and only if Cn is FC-projective modules for all n ∈ Z,and Hom(C,Q)is exact for all finitely copresented complexes Q;It is further prove that the FC-projective complexes is a kind of exact complexes.Secondly,we prove that a complex C is Gorenstein FC-projective complexes if and only if Ci is Gorenstein FC-projective modules for all i ∈ Z,and Hom(C,M)is exact for all FC-projective complexes M;Finally,the Gorenstein FC-projective dimension of complexes are introduced and discussed. |
