This paper continues the study of codivisible modules, whose definition is a “dualization” of
Lambek's concept [4] of a divisible module relative to a torsion theory. The main purpose of …

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 R be a ring. A right R-module C is called a cotorsion module if Ext1R (F, C)= 0 for any flat
right R-module F. In this paper, we first characterize those rings satisfying the condition that …

Let R be a ring, C be a left R-module and S= End R (C). When C is semidualizing, the
Auslander class AC (S) and the Bass class ℬ C (R) associated with C have been the subject …

Over any left and right self-injective ring R the R-dual functors ()* between R-Mod and Mod-
R are exact, and hence so are the double R-dual functors ()** on each of these categories. In …

A classical question for modules over an integral domain is," When is the torsion submodule
t (A) of a module A a direct summand of AT'A module is said to split when its torsion …

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

Suppose that R is a ring and that A is a chain complex over R. Inside the derived category of
differential graded R-modules there are naturally defined subcategories of A-torsion objects …

COTORSION PAIRS ASSOCIATED WITH AUSLANDER CATEGORIES Page 1 ISRAEL
JOURNAL OF MATHEMATICS 174 (2009), 253–268 DOI: 10.1007/s11856-009-0113-y …

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 …