We study which algebras have tilting modules that are both generated and cogenerated by
projective–injective modules. Crawley–Boevey and Sauter have shown that Auslander …

For a finite-dimensional algebra Λ and a nonnegative integer n, we characterize when the
set tilt n Λ of additive equivalence classes of tilting modules with projective dimension at …

In this paper, we introduce and study relative Auslander--Gorenstein pairs. This consists of a
finite-dimensional Gorenstein algebra together with a self-orthogonal module that provides a …

Let L denote a finite lattice with at least two points and let A denote the incidence K-algebra
of L over a field K. We prove that L is distributive if and only if A is an Auslander regular ring …

In this paper, we study a relationship between tilting modules with finite projective dimension
and dominant dimension with respect to injective modules as a generalization of results of …

We introduce the class of dominant Auslander-Gorenstein algebras as a generalisation of
higher Auslander algebras and minimal Auslander-Gorenstein algebras, and give their …

We give new properties of algebras with finite self-injective dimension coinciding with the
dominant dimension d≥ 2, which are called minimal Auslander–Gorenstein algebras in the …

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 …

The aim of this paper is to give a unification of the theory of (co) tilting modules and (higher)
Auslander correspondence by using faithfully balanced modules (ie, faithful modules with …

Over a finite-dimensional algebra A, simple A-modules that have projective dimension one
have special properties. For example, Geigle-Lenzing studied them in connection to …