Auslander–Reiten's generalized Nakayama conjecture

Let $\Lambda$ be an artin algebra. An indecomposable injective module is an injective $\Lambda$-module that cannot be written as a direct sum of two nonzero submodules.

Auslander–Reiten's generalized Nakayama conjecture. Any indecomposable injective $\Lambda$-module appears as a direct summand in the minimal injective resolution of $\Lambda$.

This conjecture is one of the formulations of the generalized Nakayama conjecture and is equivalent, for all artin algebras, to the Auslander–Reiten conjecture stated below.