Document Type: Original Manuscript


Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395- 4697, Tehran, Iran.


There are remarkable relations between the graded homological dimensions and the ordinary homological dimensions. In this paper, we study the injective dimension of a complex of graded modules and derive its some properties. In particular, we define the $^*$dualizing complex for a graded ring and investigate its consequences.