We introduce the notion of relative singularity category with respect to a self‐orthogonal
subcategory ω of an abelian category. We introduce the Frobenius category of ω‐Cohen …

A left and right Noetherian ringRis called Gorenstein if bothRRandRRhave finite injective
dimensions. These rings were studied by Bass for the commutative case and Iwanaga for …

For a commutative ring R and a faithfully flat R-algebra S we prove, under mild extra
assumptions, that an R-module M is Gorenstein flat if and only if the left S-module S⊗ RM is …

Let $ A $, $ B $ be two rings and $ T=\left (\begin {smallmatrix} A & M 0 & B\end
{smallmatrix}\right) $ with $ M $ an $ A $-$ B $-bimodule. Given two complete hereditary …

We prove that if the Frobenius functor F (from the category of left R-modules to the category
of left S-modules) is faithful, then for any R-module X, the Gorenstein flat dimension of X is …

It is an old observation of Eckmann-Hilton [21], that the homotopy theory of topological
spaces has an algebraic analogue in the module category of a ring. Inspired by the work of …

Introduction to Abelian Model Structures and Gorenstein Homological Dimensions provides
a starting point to study the relationship between homological and homotopical algebra, a …

Let A be an associative ring with identity, K (FlatA) the homotopy category of flat modules
and Kp (FlatA) the full subcategory of pure complexes. The quotient category K (FlatA)/Kp …

The local structure of homomorphisms of commutative noetherian rings is investigated from
the point of view of dualizing complexes. A concept of finite Gorenstein dimension, which …

This is the second part of a series of papers devoted to develop Homotopical Algebraic
Geometry. We start by defining and studying generalizations of standard notions of linear …