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 …

Abstract For an Artin Algebra Λ of finite representation type, the category Λ-mod, considered
as a ring with several objects, has Krull dimension zero. Contrary, for a wild hereditary Artin …

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 were introduced by Auslander and Reiten. Their significant
importance in the representation theory of Artin algebras and groups is well-known in the …

The main objective of this note is to characterize the irreducible morphisms of a class C. As it
is well known, these objects played a crucial role for the development of the modern theory …

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 …

Liu's Theorem Let be an artin algebra and let 0! X!ri= 1 Yi! Z! 0 be an almost split sequence
in the category of nitely generated-modules such that all Yi's are indecomposable. Suppose …

This article consists of an introduction to Iyama's higher Auslander–Reiten theory for Artin
algebras from the viewpoint of higher homological algebra. We provide alternative proofs of …

We consider A to be an artin algebra. We characterize the irreducible morphisms of left
degree two. We study the non-zero composition of irreducible morphisms in almost pre …