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Projectability and splitting property of lattice ordered groups. (English) Zbl 1080.06026
Summary: In this paper we deal with the notions of projectability, splitting property and Dedekind completeness of lattice-ordered groups, and with the relations between these notions.
##### MSC:
 06F15 Ordered groups
Full Text:
##### References:
 [1] M. Anderson, P. Conrad and O. Kenney: Splitting properties in archimedean $$\ell$$-groups. J. Austral. Math. Soc. 23 (1977), 247-256. · Zbl 0369.06012 · doi:10.1017/S1446788700018231 [2] S. J. Bernau: Lateral and Dedekind completion of archimedean lattice groups. J. London Math. Soc. 12 (1976), 320-322. · Zbl 0333.06008 · doi:10.1112/jlms/s2-12.3.320 [3] S. Bernau: Orthocompletion of lattice ordered groups. Proc. London Math. Soc. 16 (1966), 107-130. · Zbl 0136.29103 · doi:10.1112/plms/s3-16.1.107 [4] P. F. Conrad: Lateral completion of lattice ordered groups. Proc. London Math. Soc. 19 (1969), 444-480. · Zbl 0182.04803 · doi:10.1112/plms/s3-19.3.444 [5] P. F. Conrad: The essential closure of an archimedean lattice group. Duke Math. J. 38 (1971), 151-160. · Zbl 0216.03104 · doi:10.1215/S0012-7094-71-03819-1 [6] J. Jakubík: Splitting property of lattice ordered groups. Czechoslovak Math. J. 24 (1974), 257-269. · Zbl 0327.06013 [7] J. Jakubík: Strongly projectable lattice ordered groups. Czechoslovak Math. J. 26 (1976), 642-652. · Zbl 0365.06008 · eudml:12974 [8] J. Jakubík: Orthogonal hull of a strongly projectable lattice ordered group. Czechoslovak Math. J. 28 (1978), 484-504. · Zbl 0391.06014 · eudml:13083 [9] J. Jakubík: Maximal Dedekind completion of an abelian lattice ordered group. Czechoslovak Math. J. 28 (1978), 611-631. · Zbl 0432.06012 · eudml:13091 [10] J. Jakubík: Projectable kernel of a lattice ordered group. Universal Algebra and Applications. Banach Center Publ. 9 (1982), 105-112. [11] J. Jakubík: Lateral and Dedekind completion of a strongly projectable lattice ordered group. Czechoslovak Math. J. 47 (1997), 511-523. · Zbl 0897.06019 · doi:10.1023/A:1022419703077 · eudml:30381 [12] J. Jakubík and M. Csontóová: Affine completeness of projectable lattice ordered groups. Czechoslovak Math. J. 48 (1998), 359-363. · Zbl 0952.06024 · doi:10.1023/A:1022849823068 [13] J. Jakubík: Lateral completion of a projectable lattice ordered group. Czechoslovak Math. J. 50 (2000), 431-444. · Zbl 1047.06010 · doi:10.1023/A:1022491406886 · eudml:30573 [14] A. V. Koldunov and G. Ya. Rotkovich: Archimedean lattice ordered groups with the splitting property. Czechoslovak Math. J. 37 (1987), 7-18. · Zbl 0628.06014 · eudml:13616
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