From the notion of (co) generator in relative homological algebra, we present the concept of
finite balanced system $[(\mathcal {X},\omega);(\nu,\mathcal {Y})] $ as a tool to induce …

We study finiteness conditions in Grothendieck categories by introducing the concepts of
objects of type $\text {FP} _n $ and studying their closure properties with respect to short …

Recently, Gorenstein dimensions relative to a semidualizing module have been the subject
of numerous studies with interesting extensions of the classical homological dimensions …

Balanced pairs appear naturally in the realm of relative homological algebra associated with
the balance of right-derived functors of the Hom functor. Cotorsion triplets are a natural …

This thesis is comprised of three chapters. The first chapter deals with bounded complexes
of Gorenstein projective and Gorenstein injective modules. Deploying methods of relative …

We show that various methods for explicitly building resolutions of unbounded complexes in
fact fail when applied to a rather simple and explicit complex. We show that one way to …

For a local commutative Gorenstein ring R, Enochs et al. in [Gorenstein projective
resolvents, Comm. Algebra 44 (2016) 3989–4000] defined a functor Ext^ n R (−,−) and …

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

Absolutely clean and level R-modules were introduced in and used to show how Gorenstein
homological algebra can be extended to an arbitrary ring R. This led to the notion of …

We consider the equivalence from the stable module category to a subcategory $\mathcal
{L} _A $ of the homotopy category constructed by Kato. This equivalence induces a …