If M is a nonzero finitely generated module over a commutative Noetherian local ring R such
that M has finite injective dimension and finite Gorenstein dimension, then it follows from a …

We prove that for a Frobenius extension, a module over the extension ring is Gorenstein
projective if and only if its underlying module over the base ring is Gorenstein projective. For …

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

In this article we investigate the relations between the Gorenstein projective dimensions of Λ-
modules and their socles for n-minimal Auslander–Gorenstein algebras Λ. First we give a …

Let A be an Artin algebra and e an idempotent in A. It is an interesting topic to compare the
homological dimension of the algebras A, A/A e A and eAe. For example, in [2], the relation …

In this paper we develop the homological properties of the $(\mathcal {L},\mathcal {A}) $-
Gorenstein flat $ R $-modules $\mathcal {GF} _ {(\mathcal {F}(R),\mathcal {A})} $ proposed …

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 …

The theory of Gorenstein flat dimension is not complete since it is not yet known whether the
category 𝒢ℱ (R) of Gorenstein flat modules over a ring R is projectively resolving or not …

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 …

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 …