The principle "Every result in classical homological algebra should have a
counterpart in Gorenstein homological algebra" is given in [3]. There is a
remarkable body of evidence supporting this claim (cf. [2] and [3]). Perhaps
one of the most glaring exceptions is provided by the fact that tensor products
of Gorenstein projective modules need not be Gorenstein projective, even over
Gorenstein rings. So perhaps it is surprising that tensor products of
Gorenstein injective modules over Gorenstein rings of finite Krull dimension
are Gorenstein injective.