Let R be a semiprime, right Goldie ring, with semisimple Artinian right quo-tient ring Q (R). If
M is a right R-module, then the Goldie rank of M, written Grkº M, or Grk M if the context is …

, Coldie defined the reduced rank p (M) of af initely generated module M over a edprime
Coldie ring R to be the uniform dimension of M/y (If), where y is the Goldie torsion radial …

The main result of this note is that a semiprime ring with Krull dimension is a right order in a
semisimple artinian ring. In [3] this theorem is cast in the more general context of rings with …

A module M is said to be weakly injective if every finitely generated submodule of its
injective hull E (M) is contained in a submodule X of E (M) isomorphic to M. We prove that a …

Introduction. Let R be a fixed (not necessarily commutative) ring. Throughout this nte, we are
concerned with left R-modules M, A, H, Like in'Goldie [1], we shall use the following …

INTRODUCTION In [3] and [l] the author developed the theory of dual Goldie dipsruion for
unitary left R-moduleo, where R is any ring with identity. Now, suppose R is a ring not …

Let R be a ring with identity and M a unital right R-module. By the finite Goldie dimension of
M is meant the largest integer m (provided it exists) such that M contains the direct sum of m …

We find a bound for the Goldie dimension of hereditary modules in terms of the cardinality of
the generating sets of their quasi-injective hulls. Several consequences are deduced. In …

The formula dim (A+ B)= dim (A)+ dim (B)-dim (A∩ B) works when 'dim'stands for the
dimension of subspaces A, B of any vector space. In general, however, it does no longer …

Recently Tachikawa[8] has proved that, if R is a ring of dominant dimension•† 1, then domi.
dim. RR•† 2 if and only if the injective hull E (RR) of RR has the double centralizer property …