Tilting modules and dominant dimension with respect to injective modules

Takahide Adachi, Mayu Tsukamoto

Published 2019-02-25Version 1

In this paper, we study a relationship between tilting modules with finite projective dimension and dominant dimension with respect to injective modules as a generalisation of results of Crawley-Boevey--Sauter, Nguyen--Reiten--Todorov--Zhu and Pressland--Sauter. Moreover, we give characterisations of $n$-almost Auslander--Gorenstein algebras and $n$-almost Auslander algebras by the existence of tilting modules. As an application, we describe a sufficient condition of $1$-almost Auslander algebras to be strongly quasi-hereditary by comparing such tilting modules and characteristic tilting modules.