We extend the definition of a semidualizing module to general associative rings. This
enables us to define and study Auslander and Bass classes with respect to a semidualizing …

Starting from the notion of totally reflexive modules, we survey the theory of Gorenstein
homological dimensions for modules over commutative rings. The account includes the …

We introduce the notion of balanced pair of additive subcategories in an abelian category.
We give sufficient conditions under which a balanced pair of subcategories gives rise to a …

We investigate the properties of categories of GC-flat R-modules where C is a semidualizing
module over a commutative noetherian ring R. We prove that the category of all GC-flat R …

In the derived category of a commutative noetherian ring, we explicitly construct a silting
object associated with each sp-filtration of the Zariski spectrum satisfying the" slice" …

Auslander conjectured that every Artin algebra satisfies a certain condition on vanishing of
cohomology of finitely generated modules. The failure of this conjecture—by a 2003 …

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 …

Auslander's depth formula for pairs of Tor-independent modules over a regular local ring,
depth (M⊗ RN)= depth M+ depth N− depth R, has been generalized in several directions; …

A central problem in the theory of Gorenstein dimensions over commutative noetherian rings
is to find resolution-free characterizations of the modules for which these invariants are finite …

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 …