Indecomposable modules over pure semisimple hereditary rings

NV Dung, JL García - Journal of Algebra, 2012 - Elsevier
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 …

[HTML][HTML] Preinjective modules over pure semisimple rings

NV Dung, JL García - Journal of Pure and Applied Algebra, 2008 - Elsevier
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 …

[HTML][HTML] Strong preinjective partitions and almost split morphisms

NV Dung - Journal of Pure and Applied Algebra, 2001 - Elsevier
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 …

A key module over pure-semisimple hereditary rings

LA Hügel - Journal of Algebra, 2007 - Elsevier
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 …

On the endofiniteness of a key module over pure semisimple rings

N Dung, J García - Proceedings of the American Mathematical Society, 2010 - ams.org
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 …

Locally split submodules and modules with perfect endomorphism rings

G Azumaya - Non-Commutative Ring Theory: Proceedings of a …, 2006 - Springer
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 …

Definable subcategories over pure semisimple rings

NV Dung, JL Garcia - Journal of Algebra and Its Applications, 2012 - World Scientific
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 …

Endoproperties of modules and local duality

NV Dung, JL García - Journal of Algebra, 2007 - Elsevier
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 …

[PDF][PDF] Indecomposable decompositions of finitely presented pure-injective modules

JLG Pardo, PAG Asensio - Journal of Algebra, 1997 - core.ac.uk
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 …

[HTML][HTML] Equivalence of some homological conditions for ring epimorphisms

A Facchini, Z Nazemian - Journal of Pure and Applied Algebra, 2019 - Elsevier
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 …