  A commutative noetherian ring with a dualizing complex is Gorenstein if and
only if every acyclic complex of injective modules is totally acyclic. We
extend this characterization, which is due to Iyengar and Krause, to arbitrary
commutative noetherian rings, i.e. we remove the assumption about a dualizing
complex. In this context Gorenstein, of course, means locally Gorenstein at
every prime.

Commutative Algebra