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Maximal Dedekind completion of a half lattice ordered group. (English) Zbl 0948.06011
The notion of half partially ordered group and, in particular, of half lattice-ordered group is due to M. Giraudet and F. Lucas [Fundamenta Math. 139, 75-89 (1991; Zbl 0766.06014)]. The author [Math. Slovaca 46, 379-390 (1996; Zbl 0888.06009)] studied the maximal Dedekind completion of a half partially ordered group \(G\). In the present paper he shows that in the particular case when \(G\) is a half lattice-ordered group, its maximal Dedekind completion \(M_h(G)\) can be obtained by a simpler construction than that which has been used in his previous paper for half partially ordered groups. The small direct product \((s)\prod _{i\in I} G_i\) of half lattice-ordered groups \(G_i\) was investigated by the reviewer [Czechoslovak Math. J. 46, 745-767 (1996; Zbl 0879.06011)]. The present author shows that if \(G=(s)\prod _{i\in I} G_i\), then \(M_h(G)=\prod _{i\in I} M_h(G_i)\).

06F15 Ordered groups
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