In these expository notes I discuss several concepts and results in the theory of modules
over commutative rings, revolving around the Gorenstein dimension of modules. Some of …

A result of Foxby states that if there exists a complex with finite depth, finite flat dimension,
and finite injective dimension over a local ring R, then R is Gorenstein. In this paper we …

Let (R, m) be a local ring, and let C be a semidualizing R-module. In this paper, we are
concerned with the C-injective and GC-injective dimensions of certain local cohomology …

Homological dimensions and Macaulay rings Page 1 Pacific Journal of Mathematics
HOMOLOGICAL DIMENSIONS AND MACAULAY RINGS GERSON LOUIS LEVIN AND …

Let R be a commutative Noetherian ring and let C be a semidualizing R-module. It is proved
that FPD (R)= sup {GPC− pd R (M)| M∈ BC (R) and GPC− pd R (M)<∞}, which is a …

Let (R, m) be a commutative Noetherian local ring of Krull dimension d, and let C be a
semidualizing R-module. In this paper, it is shown that if R is complete, then C is a dualizing …

Let R be a commutative Noetherian ring. If cmd R≤ 1, then it is shown that for any R-module
the large restricted injective dimension is a refinement of the Gorenstein injective dimension …

A question of Avramov and Foxby concerning injective dimension of complexes is settled in
the affirmative for the class of noetherian rings. A key step in the proof is to recast the …

For finitely generated modules $ M $ and $ N $ over a commutative Noetherian local ring $
R $, we give various sufficient criteria for detecting freeness of $ M $ or $ N $ via vanishing …

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 …