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 …

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 …

However, some aspects of the classical theory can be extended to infinitely generated
modules over arbitrary rings. In this paper, we will consider such an aspect: the relation of …

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 …

We prove a generalization of the flat cover conjecture by showing for any ring R that (1) each
(right R-) module has a Ker Ext (−, C)-cover, for any class of pure-injective modules C, and …

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 …

Cotilting Modules Are Pure-Injective Page 1 PROCEEDINGS OF THE AMERICAN
MATHEMATICAL SOCIETY Volume 131, Number 12, Pages 3665-3672 S 0002-9939(03)06938-7 …

A classic result by Bass says that the class of all projective modules is covering if and only if
it is closed under direct limits. Enochs extended the if-part by showing that every class of …

This paper is devoted to the study of flat module representations. We characterize such
representations for quivers not containing the path·•→•(the so called rooted quivers). Then …

Relative coherence and preenvelopes Page 1 manuscripta math. 81, 243- 262 (1993)
manuscripta mathematica 9 Springer rlag 1993 RELATIVE COHERENCE AND …