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Discussiones Mathematicae General Algebra and Applications 22(2) (2002) 141-152
DOI: https://doi.org/10.7151/dmgaa.1053

LEXICO EXTENSION AND A CUT COMPLETION OF A HALF l-GROUP

Stefan Cernák Department of Mathematics, Faculty of Civil Engineering Technical University Vysokoskolská 4, SK-042 02 Kosice, Slovakia e-mail: svfkm@tuke.sk

Milan Demko Department of Mathematics, FHPV PU 17 Novembra 1, SK-081 16 Presov, Slovakia e-mail: demko@unipo.sk

Abstract

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.

2000 AMS Mathematics Subject Classification: Primary 06F15; Secondary 06F20.

References

[1] R.N. Ball, The structure of the α-completion of a lattice ordered group, Houston J. Math. 15 (1989), 481-515.

[2] P. Conrad, Lattice Ordered Groups, Tulane University, New Orleans, LA, 1970.

[3] M.R. Darnel, Theory of Lattice Ordered Groups, M. Dekker, Inc., New York 1995.

[4] M. Giraudet and F. Lucas, Groupes à moitié ordonnés, Fund. Math. 139 (1991), 75-89.

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

Received 27 May 2002
Revised 27 November 2002