Value in a lattice-ordered group
= Value in a lattice-ordered group
A value of $g\ne1$ is a <convex lattice subgroup> maximal among those omitting $g$. <Zorn's lemma> supplies a value: the union of a chain of convex lattice subgroups omitting $g$ still omits $g$. Such subgroups are prime. Their unique cover is the smallest convex lattice subgroup properly containing them.