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 …

Any finitely generated module M over a local ring R is endowed with a complete intersection
dimension CI-dim RM and a Gorenstein dimension G-dim RM. The Gorenstein dimension …

Let R be a ring such that all flat R-modules have finite strongly FP-injective dimension. We
obtain that the class of all Gorenstein projective modules forms a left-hand class of complete …

Given a semidualizing module C over a commutative Noetherian ring, Holm and Jørgensen
[Semi-dualizing modules and related Gorenstein homological dimensions, J. Pure Appl …

Given a homomorphism of commutative noetherian rings R→ S and an S-module N, it is
proved that the Gorenstein flat dimension of N over R, when finite, may be computed locally …

It is well-known that the weak global dimension of a ring does not exceed its global
dimension. Christensen et al. obtained a corresponding result in Gorenstein setting for …

Let (R, 𝔪) be a commutative Noetherian local ring and M an R-module which is relative
Cohen-Macaulay with respect to a proper ideal 𝔞 of R, and set n:= ht M𝔞. We prove that …

Let R→ S be a ring homomorphism. We consider the relationships of the Gorenstein
dimensions of an R-complex X (possibly unbounded) with those of the S-complexes R Hom …

We investigate the relationship between the level of a bounded complex over a commutative
ring with respect to the class of Gorenstein projective modules and other invariants of the …

In this paper, we define a homological invariant for finitely generated modules over a
commutative noetherian local ring, which we call upper Cohen-Macaulay dimension. This …