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 …

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 …

We show that every flat quasi-coherent sheaf on a quasi-compact quasi-separated scheme
is a directed colimit of locally countably presentable flat quasi-coherent sheaves. More …

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 …

This paper is a follow-up to arXiv: 2212.09639. We consider two algebraic settings of
comodules over a coring and contramodules over a topological ring with a countable base …

Homological algebra originated in late 19th century topology. Homological studies of
algebraic objects, such as rings and modules, only got under way in the middle of the 20th …

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 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 …

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 the …