Let R and S be arbitrary rings and let CSR be a semidualizing bimodule, and let 𝒜 C⁢(R op)
and ℬ C⁢(R) be the Auslander and Bass classes, respectively. Then both pairs (𝒜 C⁢(R …

The aim of this paper is to introduce the concept of right and left semidualizing adjoint pair of
functors and study its main properties. This concept generalizes the concept of …

As a generalization of a resolving subcategory, which was introduced by Auslander and
Bridger in [2], the notion of a quasi-resolving subcategory of an abelian category is …

Given an integer N≧2 and a self-orthogonal subcategory W of an abelian category A, we
investigate the W-Gorenstein N-complexes. We show that an N-complex G is W-Gorenstein …

Let R be a commutative Noetherian ring, and let C be a semidualizing R-module. For R-
modules M and N, the notions grade PC (M, N) and grade IC (M, N) are introduced as the …

Inspired in part by recent work of\v {S} aroch and\v {S}\v {t} ov\'{\i}\v {c} ek in the setting of
Gorenstein homological algebra, we extend the notion of Foxby-Golod ${\rm G_C} …

Abstract Let T=(R 0 CS) be a formal triangular matrix ring with C a semidualizing (S, R)-
bimodule. It is proven that (1) A left S-module M in Bass class is C-torsionless (resp. C …

We introduce and study" quasidualizing" modules over a commutative local noetherian ring
R. An artinian R-module T is quasidualizing if the homothety map [special characters …

Inspired in part by recent work of Šaroch and Štovıcek in the setting of Gorenstein
homological algebra, we extend the notion of Foxby-Golod GC-dimension of finitely …

Let $\A $ be an abelian category, and $\V $, $\W $ two additive full subcategories of $\A $.
We introduce and study the $\V\W $-Gorenstein subcategory of $\A $, which unifies many …