Let Λ be a ring with unit. If A is a left Λ-module, the dimension of A (notation: 1. dimΛA) is
defined to be the least integer n for which there exists an exact sequence0→ Xn→…→ X0→ …

In Theorem 2 of [3] it was shown that if 0 is rc-dimensional, then O [x] is at least (rc+ 1)-
dimensional and at most (2n+ 1)-dimensional: here, as throughout, x is an indeterminate …

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 …

Let R be an arbitrary, not necessarily commutative ring with an identity element. A left A-
module Α Φ 0 is said to have homological dimension n, denoted l. dh^ A), if A has a …

Introduction. This paper is devoted primarily to the study of commuta-tive noetherian local
rings. The main task is to compare purely algebraic properties with properties of a …

[1; 2; 3]. A module will be said to have dimension n if it has a basis of length w, and if all of its
bases are of the same length. A ring A will be called dimensional if all finitely based …

THROUGHOUT this paper we shall be considering Artinian modules over quasi local
commutative rings. We shall define a Krull dimension for these modules which will be dual to …

Page 1 NUMBER I77 T PH TO X /\!tal r" < - c: * Lu - -: *- < > KR Goodedr! and Ann K. Boyle
Dimension theory for nonsingular injective modules N/UEN/UOIRS OF THE AN/UERICAN N/UATHEN/UATICAL …

In recent works by Eilenberg Nagao and Nakayama [# I, Jans and Nakayama [8], Harada [7],
and Zaks [II] the problem of characterizing semi-primary rings all of whose residue rings …

In [I], Gabriel discussed a “Krull dimension” for rings and modules, but here we prefer to call
it the Gabriel dimension, reserving the name Krull dimension for the notion defined in [7] and …