We show that if a class of modules is closed under pure quotients, then it is precovering if
and only if it is covering, and this happens if and only if it is closed under direct sums. This is …

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 …

Module theory provides a general framework for the study of linear representations of
various mathematical objects. For example, given a field K, representations of a quiver Q …

Let be a finite direct sum of modules. We prove:(i) If Mi is radical Mj-projective for all j> i and
each Mi is H-supplemented, then M is H-supplemented.(ii) If all the Mi are relatively …

Complete cotorsion pairs are among the main sources of module approximations. Given a
ring R and a cotorsion pair ℭ=(𝒜, ℬ), we consider closure properties of the classes 𝒜 and ℬ …

Covers and Directed Colimits Page 1 Algebr Represent Theor (2006) 9: 423–430 DOI
10.1007/s10468-006-9030-5 Covers and Directed Colimits Robert El Bashir Received: 1 …

We generalize Hill's lemma in order to obtain a large family of C-filtered submodules from a
single C-filtration of a module. We use this to prove the following generalization of …

We introduce the notion of a duality pair and demonstrate how the left half of such a pair is"
often" covering and preenveloping. As an application, we generalize a result by Enochs et …

We relate the theory of envelopes and covers to tilting and cotilting theory, for (infinitely
generated) modules over arbitrary rings. Our main result characterizes tilting torsion classes …

We prove that all $ n $-cotilting $ R $-modules are pure-injective for any ring $ R $ and any
$ n\ge 0$. To achieve this, we prove that ${^{\perp _1} U} $ is a covering class whenever $ U …