Uniformly Hyperarchimedean Lattice-Ordered Groups

An abelian ℓ-group with strong unit (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\user1{\mathcal{L}}_1 $\end{document}-object) G is hyperarchimedean (HA) iff G ≤ C(YG) (the ℓ-group of real continuous functions on the maximal ideal space, YG) with λ(g) = inf{ ∣ g(x) ∣ ≠ 0} > 0 for each 0 ≠ g ∈ G. In case inf{λ(g):0 ≠ g ∈ G} > 0, we call Guniformly hyperarchimedean (UHA). This paper: examines the structure of the UHA groups in detail; shows that UHA solves the problem: when is an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\user1{\mathcal{L}}_1 $\end{document}-product HA?; describes completely the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\user1{\mathcal{L}}_1 $\end{document} − HSP-classes which are contained in HA. Final remarks detail the connection with MV-algebras.