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 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 …

In this article, we establish, as a generalization of a result on the classical homological
dimensions of commutative rings, an upper bound on the Gorenstein global dimension of …

In this paper, let R be a commutative ring and C a semidualizing module. We investigate the
(weak) C-Gorenstein global dimension of R and we get a simple formula to compute the C …

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 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 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 …

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 …

We present an alternative way of measuring the Gorenstein projective (resp., injective)
dimension of modules via a new type of complete projective (resp., injective) resolutions. As …

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 …