Finiteness of Gorenstein injective dimension of modules

The Chouinard formula for the injective dimension of a module over a noetherian ring is extended to Gorenstein injective dimension. Specifically, if M is a module of finite positive Gorenstein injective dimension over a commutative noetherian ring R, then its Gorenstein injective dimension is the supremum of depth R(p) - width R(p) M(p), where p runs through all prime ideals of R. It is also proved that if M is finitely generated and non-zero, then its Gorenstein injective dimension is equal to the depth of the base ring. This generalizes the classical Bass formula for injective dimension.