We extend the definition of a semidualizing module to general associative rings. This
enables us to define and study Auslander and Bass classes with respect to a semidualizing …

In this article we extend the results about Gorenstein modules and Foxby duality to a non-
commutative setting. This is done in § 3 of the paper, where we characterize the Auslander …

We introduce the notion of a duality pair and demonstrate how the left half of such a pair is"
often" covering and preenveloping. As an application, we generalize a result by Enochs et …

Let R be a ring. We prove that the homotopy category K (R-Proj) is always \aleph_1-
compactly generated, and, depending on the ring R, it may or may not be compactly …

Let $ R $ be a commutative Noetherian ring. We study $ R $–modules, and complexes of
such, with excellent duality properties. While their common properties are strong enough to …

In 1966, Auslander introduced the notion of the $ G $-dimension of a finitely generated
module over a Cohen-Macaulay noetherian ring and found the basic properties of these …

Given two ringsRandS, we study the category equivalences T⇄ Y, where T is a torsion class
ofR-modules and Y is a torsion-free class ofS-modules. These equivalences correspond to …

It is not known whether modules over an arbitrary ring have flat covers, however for certain
modules over commutative noetherian rings they can be shown to exist. These covers, in …

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 …

Generic modules were introduced by Crawley-Boevey in order to provide a better
understanding of finite-dimensional algebras of tame representation type. In fact he has …