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Discussiones Mathematicae General Algebra and Applications 23(1) (2003) 19-30
DOI: https://doi.org/10.7151/dmgaa.1061

ON ABSOLUTE RETRACTS AND ABSOLUTE CONVEX RETRACTS IN SOME CLASSES OF l-GROUPS

 Ján Jakubík

Matematický ústav SAV,
Gresákova 6, 040 01 Kosice, Slovakia
email: kstefan@saske.sk

Abstract

By dealing with absolute retracts of l-groups we use a definition analogous to that applied by Halmos for the case of Boolean algebras. The main results of the present paper concern absolute convex retracts in the class of all archimedean l-groups and in the class of all complete l-groups.

Keywords: l-group, absolute retract, absolute convex retract, archimedean l-group, complete l-group, orthogonal completeness.

2000 Mathematics Subject Classification: 06F20, 06F15.

References

[1]	P. Conrad, Lattice Ordered Groups, Tulane University, New Orleans, LA, 1970.
[2]	P. Conrad, The essential closure of an archimedean lattice-ordered group, Duke Math. J. 38 (1971), 151-160.
[3]	P. Halmos, Injective and projective Boolean algebras, p. 114-122 in: ``Lattice Theory" (R.P. Dilworth, editor), Amer. Math. Soc., Providence, RI,1961.
[4]	J. Jakubík, Splitting property of lattice ordered groups, Czechoslovak Math. J. 24 (1974), 257-269.
[5]	J. Jakubík, Orthogonal hull of a strongly projectable lattice ordered group, Czechoslovak Math. J. 28 (1978), 484-504.
[6]	J. Jakubík, Retracts of abelian cyclically ordered groups, Archivum Math. (Brno) 25 (1989), 13-18.
[7]	J. Jakubík, Retracts of abelian lattice ordered groups, Czechoslovak Math. J. 39 (1989), 477-489.
[8]	J. Jakubík, Retract varieties of lattice ordered groups, Czechoslovak Math. J. 40 (1990), 104-112.

Received 21 October 2002