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 …

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 …

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 …

Over a commutative noetherian ring R of finite Krull dimension, we show that every complex
of flat cotorsion R-modules decomposes as a direct sum of a minimal complex and a …

This expository article sets forth a self-contained and purely algebraic proof of a deep result
of Quillen stating that the category of simplicial commutative algebras over a commutative …

We develop the theory of trace modules up to isomorphism and explore the relationship
between preenveloping classes of modules and the property of being a trace module …

We construct a non-affine analogue of the singularity category of a Gorenstein local ring.
With this, Buchweitz's classic equivalence of three triangulated categories over a Gorenstein …

For a commutative ring S and self-orthogonal subcategory C of Mod (S), we consider matrix
factorizations whose modules belong to C. Let f∈ S be a regular element. If f is M-regular for …

Let. This improves a result of Christensen, Iyengar and Marley by lowering the bound on n.
We also improve existing results on Tor-rigidity. This progress is driven by the existence of …