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 …

This book provides a unified approach to much of the theories of equivalence and duality
between categories of modules that has transpired over the last 45 years. In particular …

We describe the structure of all cotilting and partial cotilting groups, and of all cotilting torsion-
free classes of groups. Under V= L, we also describe all tilting and partial tilting groups. As a …

Precovers and preenvelopes were introduced in the early eighties by Enochs [48] and,
independently, by Auslander and Smalø [16]. Enochs gave a general definition in terms of …

Over an arbitrary ring, we consider cotilting modules endowed with some finiteness
conditions. We show that they correspond to pairs of dualities between certain cat-egories …

Let R and S be arbitrary associative rings. Given a bimodule RWS, we denote by Δ? and Γ?
the functors Hom?(−, W) and Ext1?(−, W), where?= R or S. The functors ΔR and ΔS are right …

Tilting modules generalize projective generators and may be characterized either by
weakened generating and projectivity conditions or else by equivalences they define …

Hereditary Cotilting Modules Page 1 Ž . Journal of Algebra 238, 462478 2001 doi:10.1006rjabr.2000.8621,
available online at http:rrwww.idealibrary.com on Hereditary Cotilting Modules Francesca …

When T is a ring extension of R, conditions are found to insure that properties related to
Morita duality pass from a right R-module W to the induced right T-module Hom R (T, W). For …

In this paper, we firstly give some basic properties on quasi-cotilting modules. With the help
of these properties, we obtain a Quasi-cotilting Theorem (see Theorem 2.8). In particular, the …