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 …

We show that an iteration of the procedure used to define the Gorenstein projective modules
over a commutative ring R yields exactly the Gorenstein projective modules. Specifically …

We introduce and investigate the notion of 𝐺𝐶-projective modules over (possibly non-
Noetherian) commutative rings, where 𝐶 is a semidualizing module. This extends Holm and …

Let A be an abelian category and C an additive full subcategory of A. We provide a method
to construct a proper C-resolution (resp. coproper C-coresolution) of one term in a short …

We introduce the notion of a duality pair and demonstrate how the left half of such a pair is"
often" covering and preenveloping. As an application, we generalize a result by Enochs et …

Let W be a self-orthogonal class of left R-modules. We introduce and study W-Gorenstein
modules as a common generalization of some known modules such as Gorenstein …

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 …

Let S and R be rings and SCR a semidualizing bimodule. We investigate the relation
between the GC-syzygy with the C-syzygy of a module as well as the relation between the …

Semidualizing modules have been found to be useful for several constructions in
homological algebra. Introduced by Foxby, Vasconcelos, Golod, and Wakamatsu. Studied …

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 …