Uniformly Hyperarchimedean Lattice-Ordered Groups

An abelian ?-group with strong unit ((user1{mathcal{L}}_1 )-object) G is hyperarchimedean (HA) iff G?≤?C(YG) (the ?-group of real continuous functions on the maximal ideal space, YG) with λ(g)?=?inf{?∣?g(x)?∣?≠?0}?>?0 for each 0?≠?g?∈?G. In case inf{λ(g):0?≠?g?∈?G}?>?0, we call G uniformly hyperarchimedean (UHA). This paper: examines the structure of the UHA groups in detail; shows that UHA solves the problem: when is an (user1{mathcal{L}}_1 )-product HA?; describes completely the (user1{mathcal{L}}_1 )???HSP-classes which are contained in HA. Final remarks detail the connection with MV-algebras.