Hyperarchimedean coproducts

In the category of archimedean lattice-ordered groups with strong unit, the Yosida representation provides an insightful description of coproducts and the condition that an object be hyperarchimedean. These are combined to yield a criterion that a coproduct be hyperarchimedean and this is applied, viz .: G ∐ G is hyperarchimedean if and only if G is Specker (here meaning an ℓ-group of real-valued step functions). G ∐ H is hyperarchimedean for every hyperarchimedean H if and only if G is Specker and rational-valued. If { G i } I is a collection of Specker groups, then ∐ I G i is Specker, thus hyperarchimedean. If ∐ I H i is hyperarchimedean, then the non-Specker H i number at most c and satisfy a condition of rational-linear independence of values.