Let R be a left Noetherian ring, S a right Noetherian ring and R ω a Wakamatsu tilting
module with S= End (R ω). We introduce the notion of the ω-torsionfree dimension of finitely …

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 …

Let R be a left noetherian ring, S a right noetherian ring and UR a generalized tilting module
with S= End (UR). The injective dimensions of UR and US are identical provided both of …

We apply tilting theory to study modules of finite projective dimension. We introduce the
notion of finite and cofinite type for tilting and cotilting classes of modules, respectively …

Chapter 17 Wakamatsu Tilting Modules, U-Dominant Dimension, and k-Gorenstein Modules
Zhaoyong Huang Department of Mathematics, Nanjing University, Nanjing 210093, People's …

Let R be a left coherent ring, Rω a Wakamatsu tilting module and S= End (Rω) a right
coherent ring. It is shown that the FP-injective dimensions of Rω and ωS are identical …

In this note we show that for a* n-module, in particular, an almost n-tilting module, P over a
ring R with A= End RP such that PA has finite flat dimension, the upper bound of the global …

We study the relative Gorenstein projective global dimension of a ring with respect to a
weakly Wakamatsu tilting module C. We prove that this relative global dimension is finite if …

Let R be a commutative Noetherian ring. It is shown that the finitely generated R-module M
with finite Gorenstein dimension is reflexive if and only if M p is reflexive for p∈ Spec (R) …

The relation between the Auslander (resp., Bass) class and the class of modules with finite
Gorenstein projective (resp., injective) dimension is well known when these mentioned …