Special-valued subgroups of lattice-ordered groups
Yuanqian Chen, Paul F. Conrad · Proceedings of the American Mathematical Society · 1999
We prove that the intersection of all maximal special-valued subgroups of a lattice-ordered group G G is the special-valued quasi-torsion radical of a lattice-ordered group G G , which extends our earlier result that the intersection of all maximal finite-valued subgroups of a lattice-ordered group G G is the finite-valued torsion radical of G G . We also show that the class A f A_f of almost finite-valued lattice-ordered groups is a quasi-torsion class, and the A f A_f quasi-torsion radical of a group is equal to the intersection of the group with the lateral completion of the finite-valued torsion radical of the group.