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Uniformly Hyperarchimedean Lattice-Ordered Groups

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Abstract

An abelian ℓ-group with strong unit (\(\user1{\mathcal{L}}_1 \)-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 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.

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Correspondence to Chawne M. Kimber.

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Hager, A.W., Kimber, C.M. Uniformly Hyperarchimedean Lattice-Ordered Groups. Order 24, 121–131 (2007). https://doi.org/10.1007/s11083-007-9062-4

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  • DOI: https://doi.org/10.1007/s11083-007-9062-4

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