Let A be an abelian category. For a pair (X, Y) of classes of objects in A, we define the weak
and the (X, Y)-Gorenstein relative projective objects in A. We point out that such objects …

In this article, the new concept of relative Gorenstein flat modules is introduced. We give a
survey of their behavior in terms of both structural and dimension properties. We relate the …

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 study the concepts of the 𝒫 C-projective and the ℐ C-injective dimensions of a module in
the noncommutative case, weakening the condition of C being semidualizing. We give the …

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 …

It is proved that any tilting adjunction is completely described by an exact category with a
coherence property and the closure condition that exact sequences are acyclic. The …

It is now well known that the conditions used by Auslander to define the Gorenstein
projective modules on Noetherian rings are independent. Recently, Ringel and Zhang …

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 …

We study the relative Gorenstein projective global dimension of a ring with respect to a
weakly Wakamatsu tilting module C. We prove that this relative global dimension is finite if …

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 …