We introduce a general version of the singular compactness theorem which makes it
possible to show that being a Σ Σ-cotorsion module is a property of the complete theory of …

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 …

We describe a general correspondence between injective (resp. projective) recollements of
triangulated categories and injective (resp. projective) cotorsion pairs. This provides a model …

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 …

We study the behaviour of modules M that fit into a short exact sequence 0→ M→ C→ M→ 0,
where C belongs to a class of modules CC, the so-called C C-periodic modules. We find a …

Over any associative ring $ R $ it is standard to derive $\mathrm {Hom} _R (-,-) $ using
projective resolutions in the first variable, or injective resolutions in the second variable, and …

In this paper, we study certain properties of modules of finite Gorenstein projective, injective
and flat dimensions. We examine conditions which imply that all Gorenstein projective …

0 Introduction 611 1 Left derived extension functors 612 2 Gorenstein injective modules 616
3 Resolutions and resolvents 620 4 The existence of Gorenstein injective modules 623 5 …

In this paper, we study a particular case of Gorenstein projective, injective, and flat modules,
which we call, respectively, strongly Gorenstein projective, injective, and flat modules. These …

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) …