We study the existence of covers and envelopes by some special functors on the category of
finitely presented modules. As an application, we characterize some important rings using …

Injective covers of modules were introduced by Enochs [5] as a categorical dual of an
injective envelope and they have been investigated by many authors. The T-torsionfree …

A morphism f: M→ N of left R-modules is a phantom morphism if for any morphism g: A→ M,
with A finitely presented, the composition fg factors through a projective module …

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 …

The use of category equivalences for the study of endomorphism rings stems from the Morita
theorem. In a sense, this theorem can be viewed as stating that if P is a finitely generated …

The category of unital modules over a ring with identity element is characterized as a
cocomplete abelian category with a progenerator. More generally, every cocomplete abelian …

We study C-covers in the context of Grothendieck categories. Namely, we analyse when a
functor between two Grothendieck categories preserves or reflects C-covers. We apply our …

If R is an associative ring with identity, a theory of minimal flat resolutions is developed in the
category ((R-mod) op, Ab) of contravariant functors G:(R-mod) op→ Ab from the category R …

Let Mod-S denote the category of S-modules, where S is a small pre-additive category.
Using the notion of relative derived categories of functor categories, we generalize Rickard's …

We prove general results about completeness of cotorsion theories and existence of covers
and envelopes in locally presentable abelian categories, extending the well-established …