For a horizontally linked module, over a commutative semiperfect Noetherian ring R, the
connections of its invariants reduced grade, Gorenstein dimension and depth are studied. It …

Our purpose in this work is multifold. First, we provide general criteria for the finiteness of the
projective and injective dimensions of a finite module $ M $ over a (commutative) …

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 …

A new homological dimension, called G*-dimension, is defined for every finitely generated
module M over a local noetherian ring R. It is modeled on the CI-dimension of Avramov …

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 …

Over a commutative noetherian ring, we introduce a generalization of Gorenstein projective
and injective modules, which we call, respectively, n-Gorenstein projective and injective …

Let (R, 𝔪) be a commutative Noetherian local ring. It is known that R is Cohen–Macaulay if
there exists either a nonzero finitely generated R-module of finite injective dimension or a …

Let 𝔞 be an ideal of a commutative Noetherian ring R and M and N two finitely generated R-
modules. Let cd𝔞 (M, N) denote the supremum of the i's such that. First, by using the theory …

A Bass Formula for Gorenstein Injective Dimension Page 1 Communications in Algebra®, 35:
1882–1889, 2007 Copyright © Taylor & Francis Group, LLC ISSN: 0092-7872 print/1532-4125 …

Given a two-sided noetherian ring $ A $ with a dualizing complex, we show that the big
finitistic dimension of $ A $ is finite if and only if every bounded below Gorenstein-projective …