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 …

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 …

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 …

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 …

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 …

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 …

In this paper we are going to use a result of H. Harada and Y. Sai concerning composition of
nonisomorphisms between indecomposable modules and the theory of almost split …

Let $0\to A\to B\xrightarrow {g} C\to 0$ be a short exact sequence in the category of finitely
generated modules over an artin algebra. Suppose also that the map g is irreducible …

Let C be a full subcategory of an abelian category A which is closed under extensions, ie, if
0-+ C,+ C,+ C,-+ 0 is an exact sequence in A with C, and C3 in C, then C, is in C. An exact …

In [5], Roiter has solved the Brauer-Thrall conjecture for finite-dimensiona algebras over
fields, which states that, if the lengths of the finitely generated indecomposable modules are …