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 …

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 …

Throughout this paper A denotes an artin algebra over a commutative artin ring R; ie, A is an
R-algebra which is finitely generated as an R-module. All A-modules are assumed to …

» decomposable. Some consequences of this classification are also stated. Throughout the
paper, rings are assumed to have an identity element, modules are unitary left modules, and …

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 …

Introduction. Let A be an artin algebra and mod A the category of finitely generated (left) A-
modules. In this paper we shall develop sane techniques for constructing almost split …

Let Λ be an artin algebra. It is shown in [4] that the module category modΛ has preprojective
and preinjective partitions and that Λ is of finite representation type if and only if either all …

Let A be an artin algebra, ie, an artin ring that is a finitely generated module over its center
R, which is an artin ring, and let mod A denote the category of finitely generated (left) A …

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 …