Auslander–Gorenstein conjecture for Artin algebras

Establish whether every Artin algebra satisfying the Auslander condition is Iwanaga–Gorenstein.

Background

The paper defines the Auslander condition for a two-sided noetherian ring by requiring that the flat dimension of the ith term in the minimal injective resolution of the regular module be at most i for every i≥0. An Artin algebra is Iwanaga–Gorenstein when it has finite self-injective dimension on both sides.

The paper proves that validity of this conjecture is preserved under Frobenius extensions of Artin algebras satisfying the generator hypothesis: if S/R is such an extension and S_R is a generator, then the conjecture holds for R if and only if it holds for S. This transfer theorem does not settle the conjecture for arbitrary Artin algebras.