Let A be an artin algebra and mod A the category of finitely generated A-modules. It is well
known that almost split sequences with indecomposable middle term exist in mod A …

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 …

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 …

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 [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 …

Let A be an artin algebra and 0~ K---, L~ M----+ 0 be a short exact sequence, but not an
almost split sequence, of finitely generated A-modules. Suppose that f is irreducible (and …

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 …

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

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 …

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 …