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 …

A central problem in the theory of Gorenstein dimensions over commutative noetherian rings
is to find resolution-free characterizations of the modules for which these invariants are finite …

Let R be a local ring and M a finitely generated R-module. The complete intersection
dimension of M–defined by Avramov, Gasharov and Peeva, and denoted–is a homological …

In this paper, we introduce quasi-Gorenstein projective and quasi-Gorenstein injective
modules, study some of their properties and investigate their behavior with respect to short …

The Auslander bound of a module can be thought of as a generalization of projective
dimension. We say that the Auslander bound of $ M $ is finite if for all finitely generated …

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 …

The Chouinard formula for the injective dimension of a module over a noetherian ring is
extended to Gorenstein injective dimension. Specifically, if $ M $ is a module of finite …

Let $ R $ be a commutative noetherian ring admitting a dualizing complex and let $\mathfrak
p $ be a prime ideal of $ R $. In this paper we investigate when $ G (R/\frak p) $ is an $ R …

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 …

GORENSTEIN INJECTIVE MODULES AND A GENERALIZATION OF ISCHEBECK FORMULA
Page 1 Journal of Algebra and Its Applications Vol. 12, No. 4 (2013) 1250197 (10 pages) c …