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 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 …

Let kG be the group algebra of a finite group G over a field k of characteristic p. For any non-
projective indecomposable right &G-module W, there is a so called Auslander-Reiten …

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 …

0-> A-> B-> C-> 0 is called an almost split sequence if a) it is not splitable, b) A and C are
indecomposable A-modules and c) if f: X-> C is not a splitable epimorphism, then there is an …

Let A be an additive k-category, ka commutative artinian ring and n> 1. We denote by Cn (A)
the category of complexes [Formula: see text] in A with Xi= 0 if i∉{1,…, n}. We see that Cn (A) …

We develop an Auslander-Reiten theory for triangulated categories which is based on
Brown's representability theorem. In a fundamental article [3], Auslander and Reiten …

Introduction. Let A be an artin algebra and mod A the category of finitely generated (left) A-
modules. In this paper we shall develop sane techniques for constructing almost split …

Let Λ be an artin algebra, and denote by mod Λ the category of finitely generated Λ-
modules. All modules we consider are finitely generated. We recall from [6] that a nonsplit …

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 …