Algebras with finite relative dominant dimension and almost n-precluster tilting modules

In this paper, we investigate the relative dominant dimension with respect to an injective module and characterize the algebras with finite relative dominant dimension. As an application, we introduce the almost n-precluster tilting module and establish a correspondence between almost n-precluster tilting modules and almost n-minimal Auslander-Gorenstein algebras. Moreover, we give a description of the Gorenstein projective modules over almost n-minimal Auslander-Gorenstein algebras in terms of the corresponding almost n-precluster tilting modules.