Gorenstein injective dimension for complexes and Iwanaga-Gorenstein rings

The main purpose of this article is to present some applications of the notion of Gorenstein injective dimension of complexes over an associative ring. Among the applications, we give some new characterizations of Iwanaga-Gorenstein rings. In particular, we show that an associative ring R is Iwanaga-Gorenstein if and only if the class of complexes of Gorenstein injective dimension less than or equal to zero and the class of complexes of finite projective dimension are orthogonal complement of each other with respect to the 'Ext' functor.