Let $ S $ and $ R $ be rings and $ _SC_R $ a (faithfully) semidualizing bimodule. We
introduce and study $ C $-weak flat and $ C $-weak injective modules as a generalization of …

A model structure on a category is a formal way of introducing a homotopy theory on that
category, and if the model structure is abelian and hereditary, its homotopy category is …

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 …

Let R and S be rings and _SC_R a faithfully semidualizing bimodule. A left S-module M is
called Ding C-projective if there exists an exact sequence of C-projective left S-modules …

We continue our work on adic semidualizing complexes over a commutative noetherian ring
R by investigating the associated Auslander and Bass classes (collectively known as Foxby …

The authors introduce and investigate the T_C-Gorenstein projective, L_C-Gorenstein
injective and H_C-Gorenstein flat modules with respect to a semidualizing module C which …

Let R be a ring, C be a left R-module and S= End R (C). When C is semidualizing, the
Auslander class AC (S) and the Bass class ℬ C (R) associated with C have been the subject …

We prove that, if $\textrm {GProj} $ is the class of all Gorenstein projective modules over a
ring $ R $, then $\mathfrak {GP}=(\textrm {GProj},\textrm {GProj}^\perp) $ is a cotorsion pair …

We prove that, for any n≥ 2, the classes of FP n-injective modules and of FP n-flat modules
are both covering and preenveloping over any ring R. This includes the case of FP∞ …

The relation between the Auslander (resp., Bass) class and the class of modules with finite
Gorenstein projective (resp., injective) dimension is well known when these mentioned …