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 …

Let R be a ring and T an (infinitely generated) tilting module. Then T is of countable type; that
is, there is a set, 𝒞, of modules possessing a projective resolution consisting of countably …

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 …

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 …

1586 COLBY AND FULLER and Ringel [12] obtained an interesting class of algebras of
finite type by calculating the tilting modules and the corresponding tilted algebras. Here we …

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 …

We study a generalization of tilting modules to modules of possibly infinite projective
dimension, introduced by Wakamatsu in [J. Algebra 114 (1988) 106–114]. In particular, we …

Let $ R $ be a ring and $\mathcal C $ be a cotilting class of $ R $–modules. Define $ A\leq B
$ by $ A\subseteq B $ and $ A, B, B/A\in\mathcal C $. Then $(\mathcal C,\leq) $ is an …

Cotilting modules and bimodules over arbitrary associative rings are studied. On the one
hand we find a connection between reflexive modules with respect to a cotilting (bi) 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 …