We study some aspects of distinguished finitely generated modules of finite injective
dimension. Following Bass' conjecture, this implies that the ring is Cohen-Macaulay. We …

Starting from the notion of totally reflexive modules, we survey the theory of Gorenstein
homological dimensions for modules over commutative rings. The account includes the …

Let (R, 𝔪) be a commutative Noetherian local ring. In this paper we prove that if R admits a
finite module of finite Gorenstein injective dimension and maximal Krull dimension then R is …

The Existence of Finitely Generated Modules of Finite Gorenstein Injective Dimension Page 1
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 134, Number 11 …

In this paper, we study the relative homological dimension based on the class of projectively
coresolved Gorenstein flat modules (PGF-modules), that were introduced by Saroch and …

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 …

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 …

We introduce and investigate the notion of $\gc $-projective modules over (possibly non-
noetherian) commutative rings, where $ C $ is a semidualizing module. This extends Holm …

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 …

COHEN-MACAULAY DIMENSION OF MODULES OVER NOETHERIAN RINGS Page 1 ROCKY
MOUNTAIN JOURNAL OF MATHEMATICS Volume 35, Number 4, 2005 COHEN-MACAULAY …