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Abstract
Almost finite-valued ℓ-groups were introduced by Chen and Conrad [CC00] in studying special-valued ℓ-subgroups of lattice-ordered groups. Among their results were that maximal special-valued ℓ-subgroups of abelian ℓ-groups must be weakly saturated, the class of almost finite-valued ℓ-groups forms a quasitorsion class, and several characterizations of almost finite-valued ℓ-groups.
In this article, we show that maximal special-valued ℓ-subgroups of representable ℓ-groups must be saturated, show that maximal almost finite-valued ℓ-subgroups of abelian ℓ-groups must be saturated, and show the finite-valued radical of an ℓ-group must be contained in all maximal almost finite-valued ℓ-subgroups. A condition is given to ensure that each maximal almost finite-valued ℓ-subgroup of an abelian ℓ-group contains a maximal finite-valued ℓ-subgroup.