248 BAER equivalence of the conditions" A is tame"," P is left noetherian" and" R is left
noetherian", P and R denoting the categories of all preprojective and regular modules …

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 this paper we find the indecomposable pure injective modules over the algebras
described in the title. For undefined terms we refer to [3] and [i]. In the latter reference many …

Let C be a skeletally small abelian category with only a finite number of non-isoaorphic
simple objects and such that each object in C has finite length. Then C has a finite number of …

This paper is based upon joint work with Maurice Auslander. It is closely related to his
lecture in the workshop at ICRA VII, and a special effort has been made to emphasize the …

Let Λ be an artin algebra, that is, an artin ring that is a finitely generated module over its
center C which is also an artin ring. We denote by mod Λ the category of finitely generated …

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 …

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 …

This paper aims to initiate a study of the representation theory of representation-finite artin
algebras in terms of the nilpotency of the radical of their module category. Firstly, we shall …

The preprojective and the preinjective partitions for an artin algebra A were defined by M.
Auslander and S. Smal@[? I. Let A be an artin algebra, let mod A be the category of finitely …