Ž. We recall that a ring R with identity is said to be of finite representation type if it is right
artinian and has only finitely many isomorphism Ž. Ž classes of finitely generated …

Precovers and preenvelopes were introduced in the early eighties by Enochs [48] and,
independently, by Auslander and Smalø [16]. Enochs gave a general definition in terms of …

Let R be a hereditary, indecomposable, left pure semisimple ring. Inspired by [I. Reiten, CM
Ringel, Infinite dimensional representations of canonical algebras, Canad. J. Math. 58 …

Let R be a right pure semisimple ring, ie, a ring R such that every right R-module is a direct
sum of finitely generated modules. It is proved that R is of finite representation type if and …

This paper is devoted to the study of the endo-structure of infinite direct sums $\bigoplus_
{i\in I} M_i $ of indecomposable modules $ M_i $ over a ring $ R $. It is centered on the …

We study rings R such that all (or certain classes) of right R-modules satisfy chain conditions
on essential endosubmodules. It is proved that if all right R-modules have DCC on essential …

We study copure semisimple Grothendieck categories, ie Krull–Schmidt categories
satisfying the artinian condition on morphisms between finitely presented indecomposable …

Let R be any ring and N=⊕ i∈ INi be a direct sum of finitely presented left R-modules Ni.
Suppose that D (N) and D (Ni) are the local duals of N and Ni for each i∈ I. We prove that …

For a left pure semisimple ring R, it is shown that the local duality establishes a bijection
between the preinjective left R-modules and the preprojective right R-modules, and any …

Let $ R $ be a left pure semisimple ring such that there are no non-zero homomorphisms
from preinjective modules to non-preinjective indecomposable modules in $ R $-mod, and …