Countably valued lattice-ordered groups

A countably valued lattice-ordered group is a lattice-ordered group in which every element has only countably many values. Such lattice-ordered groups are proven to be normal-valued and, though not necessarily special-valued, every element in a countably valuedl-group must have a special value. The class of countably valuedl-groups forms a torsion class, and the torsion radical determined by this class is anl-ideal that is the intersection of all maximal countably valued subgroups.Countably valuedl-groups are shown to be closed with respect toeventually constant sequence extensions, and it is shown that many properties of anl-group pass naturally to its eventually constant sequence extension.Presented by M. Henriksen.