ARTIN ALGEBRAS WHICH ARE EQUIVALENT TO A HEREDITARY ALGEBRA MODULO
PREPROJECTIVES A. Merklen M. Auslander and I. Reiten studied Page 1 ARTIN ALGEBRAS …

In this paper we want to give a brief and informal introduction of the notion of a preprojective
partition of ind A, the set of isomorphism classes of finitely generated indecomposable …

O. Introduction Tame hereditary Artin algebras have a lot of nice homological properties: For
instance, the categories P, Rand 1 consisting of all preprojective, regular and preinjective …

In their study of the representation theory of finite-dimensional tensor algebras Dlab and
Ringet [Ill described certain modules which they called preprojective and preinjective …

An artin algebra A is said to be equivalent to an algebra A'modulo preprojectives up to the
level n if the categories mod A/add pn (A) and mod A1/add~(A'I are equivalent, Necessary …

II. First we state Proof of Proposition i. Define~: T (A)-~ Ho~(T (A), E (R/J (R))) by [~(< f) J (~.',
f')= f (~')+~'(~)~ orX,~'~ A and f, f'~ D (A), then~ is an isomorphism of T (A)-bimodule. The …

The purpose of this paper is to study the preprojective partition of a hereditary artin algebra.
For a hereditary algebra of finite representation type, we give some numerical invariants in …

It is shown that a module over an Artin algebra is pure-projective if and only tf it is a direct
sum of tinite-dimensional indecomposable submodules. Conditions under which an …

Let A be an artin algebra over a commutative artin ring R, D the self-duality functor of a
category of finitely generated A-modules defined by D (X)= HornR (X, E (R/R~~(R)) 1, where …

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 …