Gorenstein AC-Projective Dimension Of Complexs

Let R be an associate ring.It is proved that the class of L-complete projective res-olutions is close under direct transfinite extensions.Furthermore,we prove the class of Gorenstein AC-projective modules is close under direct transfinite extensions.At the same time,the Gorenstein AC-projection dimension of the modules are given.Moreover,it is proved that any complex P ? C(P)is Gorenstein AC-projective if and only if any complex G ? C(GC)is Gorenstein AC-projective.At last,some characterizations of the Gorenstein AC-projective dimension are given.