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 …

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 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 …

The small finitistic dimension of a ring is determined as the supremum projective dimensions
among modules with finite projective resolutions. This paper seeks to establish that, for a …

Let R be a left and right Noetherian ring. We introduce the notion of the torsionfree
dimension of finitely generated R-modules. For any n≧0, we prove that R is a Gorenstein …

Assume that $ R $ is a commutative Noetherian ring with non-zero identity, $\mathfrak {a} $
is an ideal of $ R $, $ X $ is an $ R $--module, and $ t $ is a non-negative integer. In this …

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 …

Any finitely generated module M over a local ring R is endowed with a complete intersection
dimension CI-dim RM and a Gorenstein dimension G-dim RM. The Gorenstein dimension …

In this article we introduce and study the concepts of uncountably generated Krull dimension
and uncountably generated Noetherian dimension of an R-module, where R is an arbitrary …