The principle “Every result in classical homological algebra should have a counterpart in
Gorenstein homological algebra” was given by Henrik Holm. We give support to 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 …

In this note we characterize the (resp., weak) Gorenstein global dimension for an arbitrary
ring. Also, we extend the well-known Hilbert's syzygy Theorem to the weak Gorenstein …

In basic homological algebra, the projective, injective and flat dimensions of modules play
an important and fundamental role. In this paper, the closely related Gorenstein projective …

The classical global and weak dimensions of rings play an important role in the theory of
rings and have a great impact on homological and commutative algebra. In this paper, we …

In this note, we characterize the (weak) Gorenstein global dimension for arbitrary associative
rings. Also, we extend the well-known Hilbert's syzygy Theorem to the weak Gorenstein …

In this article, we investigate the change of rings theorems for the Gorenstein dimensions
over arbitrary rings. Namely, by the use of the notion of strongly Gorenstein modules, we …

A new homological dimension, called G*-dimension, is defined for every finitely generated
module M over a local noetherian ring R. It is modeled on the CI-dimension of Avramov …

Throughout this paper, if not specified otherwise, R denotes an associative ring with identity
and all modules are unital left R-modules. Every result given for left modules has a …

In this paper, we prove that the Gorenstein analogue of the well-known Auslander's theorem
on the global dimension holds true. Namely, we prove that the Gorenstein global dimension …