We show that, if T is a selfsmall and selforthogonal module over a noetherian ring R of finite
global dimension with the endomorphism ring A, then fdTA⩽ gdA⩽ idRT+ fdTA. Applying the …

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 …

INTRODUCTION. The main results of this paper show that homological dimensions over a
fully bounded noetherian (FBN) ring R may be computed using just simple R-modules, as …

The aim of this paper is twofold. On the one hand, we show that the dual Goldie dimension
codim (End (MR)) of the endomorphism ring End (MR) of a module MR can be used as 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 …

In this article, we first consider concept of small Noetherian dimension of a module, which is
dual to the small krull dimension, denoted by $ sn {\rm-dim}\, A $, and defined to be the …

M. Van den Bergh proved that if A is a left noetherian N-graded ring, and I is a graded-
injective left A-module, then the injective dimension of I in the ungraded sense is at most 1 …

It is proved that a module M over a Noetherian ring R of positive characteristic p has finite flat
dimension if there exists an integer t≥ 0 such that Tor i R (M, fe R)= 0 for t≤ i≤ t+ dim R and …

The flat dimensions of injective modules Page 1 manuscripta math. 78, 165- 177 (1993)
manuscripta mathematica Spfinger-Verlag 1~3 THE FLAT DIMENSIONS OF INJECTIVE …

If M is a nonzero finitely generated module over a commutative Noetherian local ring R such
that M has finite injective dimension and finite Gorenstein dimension, then it follows from a …