Groups in which every right order is two sided
If G is a right orderable group and every right order is two sided, then G is abelian. It follows that the free lattice-ordered group F(G) over a group G exists and is a subdirect product of ordered groups if and only if G (and hence F(G)) is a torsion-free abelian group.
scientific article; zbMATH DE number 4105035