We investigate the structure of certain almost split sequences in $\mathcal {P}(\Lambda) $,
ie, the category of morphisms between projective modules over an Artin algebra $\Lambda …

Let A be an Artin algebra. As we know, the construction of the well-known Auslander-Reiten
sequence is based on the natural (A, A)-bimodule A and the induced transpose, where the …

Let $\Lambda $ be an artin algebra or, more generally, a locally bounded associative
algebra, and $\mathcal {S}(\Lambda) $ the category of all embeddings $(A\subseteq B) …

Almost split sequences lie in the heart of Auslander-Reiten theory. This paper deals with the
structure of almost split sequences with certain ending terms in the morphism category of an …

Auslander-Reiten duality for module categories is generalized to some sufficiently nice
subcategories. In particular, our consideration works for $\mathcal {P}^{<\infty}(\Lambda) …

Let $(\mbox {mod}\Lambda',\mbox {mod}\Lambda,\mbox {mod}\Lambda'') $ be a recollement
of abelian categories for artin algebras $\Lambda'$, $\Lambda $ and $\Lambda''$. Under …

We introduce the concept of maximal orthogonal subcategories over artin algebras and
orders, and develop higher Auslander-Reiten theory on them. Auslander-Reiten theory …

We use t-structures on the homotopy category K b (R-mod) for an artin algebra R and
Wattsʼ representability theorem to give an existence proof for Auslander–Reiten sequences …

We will study the relationship of quite different objects in the theory of artin algebras, namely
Auslander-regular rings of global dimension two, torsion theories, $\tau $-categories and …

We study Auslander-Reiten theory in proper abelian subcategories of triangulated
categories with a Serre functor. To initiate this, we use approximations of a Serre functor to …