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 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 …

We compare and contrast various relative cohomology theories that arise from resolutions
involving semidualizing modules. We prove a general balance result for relative …

Among the finitely generated modules over a Noetherian ring $ R $, the semidualizing
modules have been singled out due to their particularly nice duality properties. When $ R …

Using the Morita-type embedding, we show that any exact category with enough projectives
has a realization as a (pre) resolving subcategory of a module category. When the exact …

Let A be an abelian category. A subcategory X of A is called a resolving subcategory if X is
closed under extensions and kernels of epimorphisms and contains all projective objects of …

Let 𝒜 be an abelian category having enough projective and injective objects, and let 𝒯 be
an additive subcategory of 𝒜 closed under direct summands. A known assertion is that in a …

In this article we present a systematic study of the reflexivity properties of homologically finite
complexes with respect to semidualizing complexes in the setting of nonlocal rings. One …

We introduce relative preresolving subcategories and precoresolving subcategories of an
abelian category and define homological dimensions and codimensions relative to these …

Let R be a commutative noetherian local ring, and let 𝒳 be a resolving subcategory of the
category of finitely generated R-modules. In this paper, we study modules in 𝒳 by relating …