Key points are not available for this paper at this time.
We prove that if f:R→S is a local homomorphism of noetherian local rings, and M is a non-zero finitely generated or artinian S-module whose injective dimension over R is bounded by the difference of the embedding dimensions of R and S, then M is an injective S-module and f is an exceptional complete intersection map.
Hossein Faridian (2024) studied this question.