  Auslander conjectured that every Artin algebra satisfies a certain condition
on vanishing of cohomology of finitely generated modules. The failure of this
conjecture - by a 2003 counterexample due to Jorgensen and Sega - motivates the
consideration of the class of rings that do satisfy Auslander's condition. We
call them AC rings and show that an AC Artin algebra that is left-Gorenstein is
also right-Gorenstein. Furthermore, the Auslander-Reiten Conjecture is proved
for AC rings, and Auslander's G-dimension is shown to be functorial for AC
rings that are commutative or have a dualizing complex.
