Archimedean Closed Lattice-Ordered Groups
Yuanqian Chen, Paul F. Conrad, Michael R. Darnel · Rocky Mountain Journal of Mathematics · 2004
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).