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

TL;DR

This paper explores algebras with finite relative dominant dimension, introduces almost n-precluster tilting modules, and establishes their connection to almost n-minimal Auslander-Gorenstein algebras, providing new insights into Gorenstein projective modules.

Contribution

It introduces almost n-precluster tilting modules and links them to almost n-minimal Auslander-Gorenstein algebras, advancing the understanding of algebraic structures with finite relative dominant dimension.

Findings

Characterization of algebras with finite relative dominant dimension

Establishment of a correspondence between almost n-precluster tilting modules and almost n-minimal Auslander-Gorenstein algebras

Description of Gorenstein projective modules over these algebras

Abstract

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.