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 …

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 …

We study the relations between finitistic dimensions and restricted injective dimensions. Let
R be a ring and T a left R-module with A= End RT. If RT is selforthogonal, then we show that …

Let (R, m) be a commutative Noetherian local ring, I an ideal of R and let M be a non-zero I-
cofinite R-module. In this paper we show that if M has finite injective dimension, then dim …

Following our previous work about quasi-projective dimension [11], in this paper, we
introduce quasi-injective dimension as a generalization of injective dimension. We recover …

Let (R, m) be commutative Noetherian local ring. It is shown that R is Cohen-Macaulay ring if
there exists a Cohen-Macaulay finite (ie finitely generated) R-module with finite upper …

Let (R, 𝔪) be a commutative Noetherian local ring and M an R-module which is relative
Cohen-Macaulay with respect to a proper ideal 𝔞 of R, and set n:= ht M𝔞. We prove that …

This chapter discusses a commutative noetherian local ring with maximal ideal and residue
field. The local ring has sometimes a canonical module, which is of great significance, even …

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 …

In this paper we prove that for any associative ring $ R $, and for any left $ R $-module $ M $
with finite projective dimension, the Gorenstein injective dimension $\mathrm {Gid} _R M …