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 …

We obtain various characterizations of commutative Noetherian local rings (R, m) in terms of
homological dimensions of certain finitely generated modules. Our argument has a series of …

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 …

Let 𝔞 be an ideal of a commutative Noetherian ring R and M and N two finitely generated R-
modules. Let cd𝔞 (M, N) denote the supremum of the i's such that. First, by using the theory …

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 …

A central problem in the theory of Gorenstein dimensions over commutative noetherian rings
is to find resolution-free characterizations of the modules for which these invariants are finite …

We obtain various characterizations of commutative Noetherian local rings $(R,\fm) $ in
terms of homological dimensions of certain finitely generated modules. For example, we …

Let R be a local ring and M a finitely generated R-module. The complete intersection
dimension of M–defined by Avramov, Gasharov and Peeva, and denoted–is a homological …

In this paper we prove that for any associative ring $ R $, and for any left $ R $-module $ M $
with finite projective dimension, the Gorenstein injective dimension $\mathrm {Gid} _R M …

The main aim of this paper is to obtain a dual result to the now well known Auslander-
Bridger formula for G-dimension. We will show that if R is a complete Cohen-Macaulay ring …