An R-module M is said to be an extending module if every closed submodule of M is a direct
summand. In this paper we introduce and investigate the concept of a type 2 τ-extending …

E. Matlis proved that if R is an integral domain with quotient field Q and K is the R-module
Q/R, then all torsion R-modules decompose into a direct sum of local submodules if and only …

Let R be a small preadditive category, viewed as a “ring with several objects.” A right R-
module is an additive functor from Rop to the category Ab of abelian groups. We show that …

In the category of right modules over the ring E= End R (F), where F is a free right R-module,
a torsion is defined. It is known as Tol'skaya torsion. The correlation between torsion-free E …

We study the notion (for categories of modules) dual to that of torsion radical and its
connections with projective modules. Torsion radicals in categories of modules have been …

An R-module M is said to be a C1-module if every closed submodule of M is a direct
summand. In this paper we introduce and investigate the concept of the\tau-C1 module for a …

In this paper we prove that the extension of pure injective module is pure injective if and only
if the cotorsion envelope and the pure injective envelope of any R-module M are isomorphic …

Given a ring $ R $, two classes $\mathcal A $ and $\mathcal B $ of $ R $-modules are said
to form a cotorsion pair $(\mathcal A,\mathcal B) $ in $\operatorname {Mod} R $ if $\mathcal …

Let τ be an hereditary torsion theory. For a ring with τ-Gabriel dimension, we find necessary
and sufficient conditions for the existence of a bijective correspondence between the τ …

In this article, FP-injective complexes are introduced and studied. We prove that (⊥ ℱℐ, ℱℐ)
is a hereditary cotorsion theory if and only if R is a left coherent ring, where ℱℐ denotes the …