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 …

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 …

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 …

It is well known that for a Noetherian ring R, an ideal I of R, and M a finitely generated R-
module, the local cohomology modules HiI (M) are not always finitely generated. On the …

Let R be a commutative Noetherian ring, a an ideal of R, and let M be a finitely generated R-
module. For a non-negative integer t, we prove that H_ a^ t (M) is a-cofinite whenever H_ a …

Let R be an arbitrary ring and C a complex with finite Gorenstein projective dimension (that
is, the supremum of Gorenstein projective dimension of all R-modules in C is finite). For …

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 be a complete Gorenstein local domain, 𝐽 an ideal of 𝑅 of dimension one, and 𝑁• a
complex of 𝑅-modules bounded below. In this paper, we prove that 𝑁• is a 𝐽-cofinite …

Let R be a commutative Noetherian ring and let M be a non-zero finitely generated R-
module. Let I be an ideal of R and ta non-negative integer such that dimSuppHIi (M)⩽ 1 for …

Let R be a commutative Noetherian ring of Krull dimension d admitting a dualizing complex
D and let 𝔞 be any ideal of R. We prove that is Gorenstein injective for any Gorenstein …