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Archimedean closed lattice-ordered groups. (English) Zbl 1058.06019
Authors’ abstract: We show that, if an abelian lattice-ordered group is archimedean closed, then each principal \(\ell\)-ideal is also archimedean closed. This gives a positive answer to a question raised in 1965 and hence proves that the class of abelian archimedean closed lattice-ordered groups is a radical class. We also provide some conditions for a lattice-ordered group \(F(\Delta, R)\) to be the unique archimedean closure of \(\Sigma(\Delta, R)\).

MSC:
06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
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