Nakayama conjecture on infinite dominant dimension

Prove that for any Artin algebra A, if the dominant dimension of A is infinite, then A is self-injective.

Background

Dominant dimension was introduced by Nakayama and plays a central role in representation theory of Artin algebras. Müller’s correspondence relates algebras of dominant dimension at least 2 to endomorphism algebras of generator-cogenerators, and the extreme case of infinite dominant dimension is encapsulated in the Nakayama conjecture.

The authors recall the classical formulation and context, emphasizing its status as a core problem and noting that it remains unresolved in general. They further discuss equivalent formulations via self-orthogonal generator-cogenerators.