On torsion classes of lattcie-ordered groups

We study lattice-ordered groups whose set of branch points in the root system of regular subgroups satisfies descending chain condition. We show that these lattice-ordered groups form a torsion class (D) over bar. We also show that the class of finite-valued lattice-ordered groups that are also in (D) over bar is closed with respect to lattice-ordered subgroups, and such class has a unique archimedean closure.