We generalize Ringel and Schmidmeier's theory on the Auslander–Reiten translation of the
submodule category 𝒮 2 (A) to the monomorphism category 𝒮 n (A); the category consists of …

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) …

The monomorphism category M (A, M, B) induced by a bimodule MBA is the subcategory of
Λ-mod consisting of [XY] ϕ such that ϕ: M⊗ BY→ X is a monic A-map, where Λ=[AM 0 B] …

Let A be an artin algebra and modA the category of finitely generated A-modules. Unless
stated to the contrary, by a subcategory C of a category we mean a full subcategory of an …

We study irreducible morphisms in the bounded derived category of finitely generated
modules over an Artin algebra Λ, denoted Db (Λmod), by means of the underlying category …

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 …

Given two finite dimensional algebras Λ and Γ, it is shown that Λ is of wild representation
type if and only if Γ is of wild representation type provided that the stable categories of finite …

The concept of cluster tilting gives a higher analogue of classical Auslander correspondence
between representation-finite algebras and Auslander algebras. The n-Auslander–Reiten …

We introduce a notion of generalized Auslander–Reiten duality on a Hom-finite Krull–
Schmidt exact category 𝒞. This duality induces the generalized Auslander–Reiten …

The study of the stable derived category of a finite-dimensional self-injec-tive algebra A over
a field k was begun in [7, 8]. As the name suggests, this category can be regarded as a sort …