‎ The representation theory of groups is one of the most interesting examples of the
interaction between physics and pure mathematics‎,‎ where group rings play the main role‎.‎ …

In this paper, we show that the injective dimension of all projective modules over a
countable ring is bounded by the self-injective dimension of the ring. We also examine the …

In this paper, we study certain properties of modules of finite Gorenstein projective, injective
and flat dimensions. We examine conditions which imply that all Gorenstein projective …

In this paper, we mainly investigate the $\mathfrak {X} $-Gorenstein projective dimension of
modules and the (left) $\mathfrak {X} $-Gorenstein global dimension of rings. Some …

Let R be a ring and S an excellent extension of R. In this paper we study the Gorenstein
homological dimensions over R and S. We show that if M is an S-module, then MR is …

This thesis is devoted to the study of the homological dimension, homological homogeneity
and injective homogeneity of the skew group rings, crossed products, group graded rings …

Let $ R $ be a left coherent ring. It is proven that if an $ R $-module $ M $ has a finite FP-
injective dimension, then the Gorenstein projective (resp. Gorenstein flat) dimension and the …

In this paper, we extend the well-known Hilbert's syzygy theorem to the Gorenstein
homological dimensions of rings. Also, we study the Gorenstein homological dimensions of …

Let R be a left and right ℵ0-Noetherian ring. We show that if all projective left and all
projective right R-modules have finite injective dimension, then all injective left and all …

Let 𝒜 be an abelian category and (𝒳, 𝒴) a pair of classes of objects in 𝒜. Inspired by
Bouchiba's work on generalized Gorenstein projective modules, we give a new way of …