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 …

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 …

We prove that (a) if R is a commutative coherent ring, the weak global dimension of R equals
the supremum of the flat (or (FP–) injective) dimensions of the simple R-modules;(b) if R is …

It is well-known that the weak global dimension of a ring does not exceed its global
dimension. Christensen et al. obtained a corresponding result in Gorenstein setting for …

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 …

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 …

In this note we characterize the (resp., weak) Gorenstein global dimension for an arbitrary
ring. Also, we extend the well-known Hilbert's syzygy Theorem to the weak Gorenstein …

In this note, we characterize the (weak) Gorenstein global dimension for arbitrary associative
rings. Also, we extend the well-known Hilbert's syzygy Theorem to the weak Gorenstein …

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 …