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 …

In [5J there was introduced and studied the Goldie dimension of nodular lattices
generalizing the one of nodules and its dual (see [71). This provided several applications to …

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 …

Two elementsxandyof a partially ordered setPare said to bedisjointif there is noz∈ Psuch
thatz≤ xandz≤ y. Denote by δ (P) the supremum of the cardinals κ such thatPcontains a …

In [2] RP Dilworth introduced the concept of a principal element of a multiplicative lattice and
used it to isolate a class of multiplicative lattices in which many of the important theorems of …

Let L be lattice and let I (L) be the lattice of (non-empty) ideals of L. Then the natural
embedding a~-~(a] of L into I (L) is an isomorphism if and only if every ideal of L is principal …

Introduction. The concept of purity has played a large role in the theory of Abelian groups.
We give here a definition of purity of an element in a lattice which extends the definition of …

In [Gd] Goodearl proved that if for every essential submodule N of a module MM/N is a
Noetherian module, then the module M/SocM is Noetherian. Then in [AS], Al-Khazzi and …

The class of [-modules over a given lattice ordered ring forms an equational class consisting
precisely of those lattice ordered modules that are subdirect products of totally ordered …

M. LU Í SA GALV AO(LISBOA) AND PATRICK F. SMITH(GLASGOW) We give an analogue
for complete modular lattices of the result of Goodearl who proved that an arbitrary module …