The paper deals with almost split sequences. Introduced in [2] for the category mod A of
finitely generated modules over an artin algebra A, almost split sequences were later found …

Let R be a commutative artin ring and let/i be an R-algebra which is a finitely generated R-
module. In [5] Auslander and Reiten introduced the notion of an almost split sequence in …

Almost projective modules and almost split sequences with indecomposable middle term Page 1
COMMUNICATIONS IN ALGEBRA, 8(12), 1123-1150 (1980) ALMOST PROJECTIVE MODULES …

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 …

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 …

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 …

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 …

In [3], traces of endomorphisms of semisimple modules were used to give a method for
constructing almost split sequences of finitely generated modules over an artin algebra. This …

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) …