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 …

For a dualizing module $ D $ over a commutative Noetherian ring $ R $ with identity, it is
known that its Auslander class $\mathscr {A} _D\left (R\right) $(respectively, Bass class …

In 1966, Auslander introduced the notion of the $ G $-dimension of a finitely generated
module over a Cohen-Macaulay noetherian ring and found the basic properties of these …

We apply tilting theory to study modules of finite projective dimension. We introduce the
notion of finite and cofinite type for tilting and cotilting classes of modules, respectively …

If M is a nonzero finitely generated module over a commutative Noetherian local ring R such
that M has finite injective dimension and finite Gorenstein dimension, then it follows from a …

In\cite {Ouarghi}, the authors discuss the rings over which all modules are strongly
Gorenstein projective. In this paper, we are interesting to an extension of this idea. Thus, we …

This paper generalize the idea of the authors in\cite {Bennis and Mahdou1}. Namely, we
define and study a particular case of modules with Gorenstein projective, injective, and flat …

In this article, we give a new characterization of Gorenstein projective modules. As
applications of our result, we prove that a strongly Gorenstein projective module 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 …

This paper is a continuation of the papers J. Pure Appl. Algebra, 210 (2007), 437–445 and J.
Algebra Appl., 8 (2009), 219–227. Namely, we introduce and study a doubly filtered set of …