We give a classification of all exact structures on a given idempotent complete additive
category. Using this, we investigate the structure of an exact category with finitely many …

The Auslander correspondence is a fundamental result in Auslander-Reiten theory. In this
paper we introduce the category mo d adm (E) of admissibly finitely presented functors and …

We investigate how to characterize subcategories of abelian categories in terms of intrinsic
axioms. In particular, we find axioms which characterize generating cogenerating functorially …

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 …

We study certain special tilting and cotilting modules for an algebra with positive dominant
dimension, each of which is generated or cogenerated (and usually both) by projective …

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 …

For a field R of characteristic p≥ 0 and a matrix c in the full n× n matrix algebra M n (R) over
R, let S n (c, R) be the centralizer algebra of c in M n (R). We show that S n (c, R) is 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 …

We generalize the notions of $ d $-cluster tilting pair and $ d $-Auslander exact dg category
to $ d $-precluster tilting triple and $ d $-minimal Auslander--Gorenstein exact dg category …

We introduce a new family of algebras, called Serre-formal algebras. They are Iwanaga–
Gorenstein algebras for which applying any power of the Serre functor on any …