We define and study a notion of Gorenstein projective dimension for complexes of left
modules over associative rings. For complexes of finite Gorenstein projective dimension we …

We use torsion pairs in stable categories and cotorsion pairs in modules categories to study,
in general infinitely generated, Cohen–Macaulay modules and (a generalization of) …

Let S and R be rings and SCR a semidualizing bimodule. We investigate the relation
between the GC-syzygy with the C-syzygy of a module as well as the relation between the …

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 …

In this article we extend the notion of Gorenstein injective and projective modules to that of
complexes and characterize such complexes. We prove that over an n-Gorenstein ring every …

New homotopy invariant finiteness conditions on modules over commutative rings are
introduced, and their properties are studied systematically. A number of finiteness results for …

The local structure of homomorphisms of commutative noetherian rings is investigated from
the point of view of dualizing complexes. A concept of finite Gorenstein dimension, which …

We consider the homotopy category of complexes of projective modules over a Noetherian
ring. Truncation at degree zero induces a fully faithful triangle functor from the totally acyclic …

The notions of torsion and torsion freeness have played a very important role in module
theory--particularly in the study of modules over integral domains. Furthermore, the use of …

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 …