TAG-modules with complement submodules -pure.
The almost isomorphism relation for simple regular rings.
A longstanding open problem in the theory of von Neumann regular rings is the question of whether every directly finite simple regular ring must be unit-regular. Recent work on this problem has been done by P. Menal, K. C. O'Meara, and the authors. To clarify some aspects of these new developments, we introduce and study the notion of almost isomorphism between finitely generated projective modules over a simple regular ring.
The closure of radical classes under finite subdirect products
The Construction of Almost Split Sequences, III: Modules Over Two Classes of Tame Local Algebras.
The existence of relative pure injective envelopes
Let 𝓢 be a class of finitely presented R-modules such that R∈ 𝓢 and 𝓢 has a subset 𝓢* with the property that for any U∈ 𝓢 there is a U*∈ 𝓢* with U* ≅ U. We show that the class of 𝓢-pure injective R-modules is preenveloping. As an application, we deduce that the left global 𝓢-pure projective dimension of R is equal to its left global 𝓢-pure injective dimension. As our main result, we prove that, in fact, the class of 𝓢-pure injective R-modules is enveloping.
The hulls of semiprime rings
The intersection of distinct Galois subrings is not necessarily Galois
The irreducible components of the nilpotent associative algebras.
The aim of this work is to describe the irreducible components of the nilpotent complex associative algebras varieties of dimension 2 to 5 and to give a lower bound of the number of these components in any dimension.
The Local Duality for Homomorphisms and an Application to Pure Semisimple PI-Rings
The N*-Metric Completion of Regular Rings.
The rings which are Boolean. II.
The Schur Subgroup of a Real Cyclotomic Field.
The spectrum of a Cartesian product of plural algebras
The standard form of a representation-finite algebra
The structure of Loewy modules.
The structure of primary modules
Théorème de densité de Tchebotareff et monogénéité de modules sur l'algèbre d'un groupe métacyclique
Torsion free types
Torsion modules behaving like torsion Abelian groups