If R is a hereditary left artinian ring, then R is left pure semisimple if and only if the family R-
ind of all finitely generated indecomposable left R-modules has a (unique) Ext-injective …

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 …

A family C of finitely generated indecomposable modules is said to have right almost split
morphisms if there is a right almost split morphism f: N→ M in add C for each …

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

Let M be a left module over a ring R. A submodule N of M is called locally split in M if for
each x EN there exists a homomorphism h: Mt N such that h (x)= x. It is shown that if N is …

Let R be a right pure semisimple ring, and be a family of sources of left almost split
morphisms in mod-R. We study the definable subcategory in Mod-R determined by the …

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 …

Ž. It is well known that pure-injective s algebraically compact modules behave well in
relation to direct sum decompositions. Any indecomposable wx pure-injective module has …

Abstract Let R⊆ Q be rings such that the inclusion φ: R→ Q is an epimorphism in the
category of rings and Q is flat both as a right and as a left R-module. Assume that F. dim …