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On completions of linearly ordered groups. (English) Zbl 0712.06009

This paper contains a single theorem: If G is a linearly ordered group and H a lattice-ordered group containing G as a sublattice subgroup, and if H is Dedekind-MacNeille complete, and if the order-closure of G in H is all of H, then H is isomorphic over G to the Dedekind-MacNeille completion of G. This was known previously for Archimedean G, and stands in contrast to the more general case in which G is an (Archimedean) lattice-ordered group.
Reviewer: S.McCleary

MSC:

06F15 Ordered groups
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