We establish equivalent conditions under which every object in an Abelian category has a
monic X-cover and an epic X-envelope respectively, when X is a class of objects closed …

In the general setting of Grothendieck categories with enough projectives, we prove
theorems that make possible to restrict the study of the problem of the existence of F-covers …

Using the dual of a categorical definition of an injective envelope, injective covers can be
defined. For a ring R, every left R-module is shown to have an injective cover if and only if R …

In an earlier paper the first named authors investigated rings whose kernel functors are
linearly ordered. The main tool for describing prop-erties of such rings was the filter of ideals …

Let R be a ring and M a right R-module. Several authors have considered when the module
M has the property that all modules in a specified class are M-injective. For example, Hirano …

We study, over an arbitrary ring R, a class of right modules intermediate between the
projective and the flat content modules. Over the ring of rational integers these modules are …

We study the $ t $-structure induced by an $ n $-tilting module $ T $ in the derived category
$\mathcal {D}(R) $ of a ring $ R $. Our main objective is to determine when the heart of the …

In this note we characterize those torsion theories over a semiperfect ring such that the class
of torsion free modules is closed under projective covers and the hereditary torsion theories …

Let T be a right exact functor from an abelian category ℬ into another abelian category A.
Then there exists a functor p from the product category A× ℬ to the comma category ((T↓ …

Absolutely pure modules act in ways similar to injective modules. There are conditions on a
ring which guarantee that the class of injective modules will be covering. In this article, we …