The theory of modules over a ring or algebra grew out of the study of representations.
However, as homological algebra developed, it became clear that module theory constitutes …

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 …

A morphism f: M→ N of left R-modules is a phantom morphism if for any morphism g: A→ M,
with A finitely presented, the composition fg factors through a projective module …

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Throughout the book Homological algebra, by H. Cartan and S. Eilenberg, the authors dealt
with functors defined on categories of modules over certain rings and whose values again …

There are different approaches to characterizing the structures of commutative rings: the
category of modules over commutative rings, homology theories, theories of the star …

Semidualizing modules have been found to be useful for several constructions in
homological algebra. Introduced by Foxby, Vasconcelos, Golod, and Wakamatsu. Studied …

This volume provides a comprehensive introduction to module theory and the related part of
ring theory, including original results as well as the most recent work. It is a useful and …

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 …