Since the injective envelope and projective cover were defined by Eckmann and Bas in the
1960s, they have had great influence on the development of homological algebra, ring …

Over the last few years, the study of complexes has become increasingly important. To date,
however, most of the research is scattered throughout the literature or available only as …

This book is an introduction to the theory of rings and modules that goes beyond what one
normally obtains in a graduate course in abstract algebra. The theme of the text is the …

The idea of writing this book came roughly at the time of publication of my graduate text
Lectures on Modules and Rings, Springer GTM Vol. 189, 1999. Since that time, teaching …

Using the dual of a categorical definition of an injective envelope, injective covers can be
defined. For a ring R, every left R-module is shown to have an injective cover if and only if R …

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 …

THE EXISTENCE OF GORENSTEIN FLAT COVERS Page 1 MATH. SCAND. 94 (2004), 46-62
THE EXISTENCE OF GORENSTEIN FLAT COVERS EDGAR Ε. ENOCHS, OVERTOUN ΜGJENDA …

Let A be an integral domain and K its field of fractions. An A-module E is said to be torsion
free if ax= 0 for azA, x EE implies a= 0 or x= 0. We will say that a submodule E1 of an A …

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 …

In this paper we give two different proofs that the flat cover conjecture is true: that is, every
module has a flat cover. The two proofs are of completely different nature, and, we hope, will …