Geodesic
Lexico extension and a cut completion of a half l-group
Discussiones Mathematicae. General Algebra and Applications, Tome 22 (2002) no. 2, pp. 141-152.

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The cut completi on of an hl-group G with the abelian increasing part is investigated under the assumption that G is a lexico extension of its hl-subgroup.
Keywords: half lattice ordered group, l-group, cut completion, lexico extension 
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Černák, Štefan; Demko, Milan. Lexico extension and a cut completion of a half l-group. Discussiones Mathematicae. General Algebra and Applications, Tome 22 (2002) no. 2, pp. 141-152. http://geodesic.mathdoc.fr/item/DMGAA_2002_22_2_a3/

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[5] J. Jakubík, On cut completions of abelian lattice ordered groups, Czechoslovak Math. J. 50 (125) (2000), 587-602.