Let Λ be an Artin algebra and be an object in, the morphism category of Λ. We will describe
the Auslander–Reiten translate of, ie, as an object in. It is shown that, even though there may …

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 …

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) …

If H is a hereditary abelian category with tilting object, then it is shown that H is derived
equivalent to a module category over a hereditary artin algebra provided H contains a …

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 Λ be an artin algebra. In his seminal Philadelphia Notes published in 1978, Auslander
introduced the concept of morphisms being determined by modules. Auslander was very …

We consider Λ Λ an artin algebra and n ≥ 2 n≥ 2. We study how to compute the left and
right degrees of irreducible morphisms between complexes in a generalized standard …

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 …

If $\Lambda $ is an artin algebra there is a partition of $\operatorname {ind}\Lambda $, the
category of indecomposable finitely generated $\Lambda $-modules, $\operatorname …

We study necessary and sufficient conditions for the existence of n irreducible morphisms in
the bounded derived category of an Artin algebra, with non-zero composite in the n+ 1 …