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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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##### References:
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