We study the Gorenstein weak global dimension of associative rings and its relation to the
Gorenstein global dimension. In particular, we prove the conjecture that the Gorenstein …

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 …

A locally coherent exact category is a finitely accessible additive category endowed with an
exact structure in which the admissible short exact sequences are the directed colimits of …

A recent result by J. Šaroch and J. Šťovíček asserts that there is a unique abelian model
structure on the category of left R-modules, for any associative ring R with identity, whose …

The phenomenon of periodicity, discovered by Benson and Goodearl, is linked to the
behavior of the objects of cocycles in acyclic complexes. It is known that any flat Proj …

We give necessary and sufficient conditions in order for the class of projectively coresolved
Gorenstein flat modules, PGF (respectively that of projectively coresolved Gorenstein B flat …

We introduce a refinement of the Gorenstein flat dimension for complexes over an
associative ring—the Gorenstein flat-cotorsion dimension—and prove that it, unlike the …

We introduce a notion of total acyclicity associated to a subcategory of an abelian category
and consider the Gorenstein objects they define. These Gorenstein objects form a Frobenius …

Let R be a general ring. Duality pairs of R-modules were introduced by Holm-Jørgensen.
Most examples satisfy further properties making them what we call semi-complete duality …

In this article, the new concept of relative Gorenstein flat modules is introduced. We give a
survey of their behavior in terms of both structural and dimension properties. We relate the …