Let R be a local commutative n-Gorenstein ring. The existence of the Gorenstein projective
preenvelopes for finite R-modules is known (it was proved using duality arguments). In the …

Let $ S $ and $ R $ be rings and $ _SC_R $ a (faithfully) semidualizing bimodule. We
introduce and study $ C $-weak flat and $ C $-weak injective modules as a generalization of …

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 …

Let R be a commutative noetherian local ring and consider the set of isomorphism classes of
indecomposable totally reflexive R-modules. We prove that if this set is finite, then either it …

A new homological symmetry condition is exhibited that extends and unifies several recently
defined and widely used concepts. Applications include general constructions of tilting …

We show that any module admits a presentation as the quotient of a Gorenstein projective
module by a submodule which is itself right orthogonal, with respect to the standard Ext 1 …

In this paper, we study the relative homological dimension based on the class of projectively
coresolved Gorenstein flat modules (PGF-modules), that were introduced by Saroch and …

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

The extension of scalars functor along a finite ring homomorphism is a classic example of a
functor which preserves purity and pure injectivity. We consider how this functor behaves …

Let R be a commutative Noetherian ring and C a semidualizing R-module. We obtain an
exact structure (ℋ C, 𝜀) and prove that the full subcategory ℋ C∩ 𝒢 ℱ C of ℋ C is a …