Archimedean Closed Lattice-Ordered Groups
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Rocky Mountain Mathematics Consortium
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Abstract
We show that, if an abelian lattice-ordered group is archimedean closed, then each principal l-ideal is also archimedean closed. This has given a positive answer to the question raised in 1965 and hence proved that the class of abelian archimedean closed lattice-ordered groups is a radical class. We also provide some conditions for lattice-ordered group F(Δ,R) to be the unique archimedean closure of Σ (Δ,R).
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Chen, Yuanqian, et al. “Archimedean Closed Lattice-Ordered Groups.” Rocky Mountain Journal of Mathematics, vol. 34, no. 1, Spring 2004, pp. 111–24.
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