[引用][C] The construction of almost split sequences, I

MCR Butler - Proceedings of the London Mathematical Society, 1980 - Wiley Online Library
Almost split sequences of modules were introduced and studied in the last three papers in
the series [1,..., 6] by Auslander and Reiten and, with the related simple functors and …

[引用][C] On algebras whose indecomposable modules are multiplicity-free

Z Pogorzały, A Skowroński - Proceedings of the London …, 1983 - academic.oup.com
Almost split sequences, introduced and investigated by Auslander and Reiten [2-6], form a
distinguished class of short exact sequences; amongst other properties, their end terms are …

Representation theory of artin algebras v: methods for computing aimost split sequences and irreducible morphisms

M Auslander, I Reiten - Communications in algebra, 1977 - Taylor & Francis
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 …

Uniserial functors

M Auslander, I Reiten - Representation Theory II: Proceedings of the …, 2006 - Springer
Throughout this paper modA denotes the category of finitely generated A-modules over an
artin algebra A. We say that a covariant or contravariant functor F from modA to abelian …

Almost split sequences I

M Auslander - Representations of Algebras: Proceedings of the …, 1975 - Springer
The main purpose of these talks is to in~ roduce the notion of almost split 11equences. The
first talk is devoted to giving various consequences of their e~ istence in order to indicate the …

The use of almost split sequences in the representation theory of Artin algebras

I Reiten - Representations of Algebras: Workshop Notes of the …, 2006 - Springer
Let A be an artin algebra, for example a finite dimensional algebra over a field k and C an
indecomposable nonprojective finitely generated left A-module. Then there is an exact …

[引用][C] The equivalence of certain functors occurring in the representation theory of Artin algebras and species

S Brenner, MCR Butler - Journal of the London Mathematical …, 1976 - Wiley Online Library
One of the main results of the Auslander and Reiten theory [1] of finitely generated modules
over an Artin algebra A is that there exists an operator, denoted DTr, which maps the non …

[PDF][PDF] An introduction to the representation theory of artin algebras

I Reiten - Bulletin of the London Mathematical Society, 1985 - Citeseer
The representation theory of artin algebras, as we understand it to-day, is a relatively new
area of mathematics, as most of the main developments have occurred since the late sixties …

Almost split sequences II

M Auslander, I Reiten - Representations of Algebras: Proceedings of the …, 1975 - Springer
In [1] various applications of the existence and uniqueness of almost split sequences for
artin algebras were given. These results motivate trying to get some more information on …

Representation theory of artin algebras VI: A functorial approach to aimost split sequences

M Auslander, I Reiten - Communications in algebra, 1978 - Taylor & Francis
In this pper we study the relevance of almost split sequences for the study of certain
problems in the functor categories nod (mod A) and mod (rrod A). One connection between …