The concept of the Gloldie dimension of a module has been different ways: by Fleury in [2]
and by Varadarajan in [S]. Fleury's of the lattice nature-while the character of Varadarajan's …

This dissertation reviews attempts of dualizing the Goldie dimension. Moreover we choose
one of these attempts as the dualization of Goldie dimension and study modules with this …

In the paper we use the lattice I (L) of all ideals of L. Recall that for any set S of ideals of L,/k
S=~ S and VS={xe L Ix< _ VF for some finite subset F of U s}. it is known that the lattice I (L) is …

The purpose of this note is to offer a equalization of the concept of Goldie dimension and to
prove a structure theorem (Theorem 3.1) for modules satisfying the conditions of this …

2. It was shown by P. Fleury [L] that any such module M is an irredundant sum of finitely
many hollow modules and that the number of hollow modules in any expression of M as an …

For subspaces U and V of a vector space, the formula dim (^+ V)= dim U+ dim V-dim (U flV)
is well known. The same formula also holds for composition lengths-of submodules of a …

DUAL GOLDIE DIMENSION 567 The object of the present paper is to study modules of finite
corank. It will turn out that all the results of Goldie on Goldie dimension have corresponding …

It became more and more usual, from, say, the 1970s, for each book on Module Theory, to
point out and prove some (but in no more than 15 to 20 pages) generalizations to (mostly …

There have been developed in the literature two kinds of the theory of dimensionality in
lattices, that is, one is the theory in the continuous geometries (von Neumann [13], Halperin …

1. Introduction. In [9] LH Loomis studies an abstract version of the von Neumann-Murray
dimension theory for rings of operators in Hilbert space. He takes as context a complete …