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Article

Jakubík, Ján
Affine completeness and lexicographic product decompositions of abelian lattice ordered groups. (English). Czechoslovak Mathematical Journal, vol. 55 (2005), issue 4, pp. 917-922
MSC: 06F20 | MR 2184372 | Zbl 1081.06022
Keywords:
Abelian lattice ordered group; lexicographic product decomposition; affine completeness
Summary:
In this paper it is proved that an abelian lattice ordered group which can be expressed as a nontrivial lexicographic product is never affine complete.
References:
[1] L.  Fuchs: Partially Ordered Algebraic Systems. Pergamon Press, Oxford, 1963. MR 0171864 | Zbl 0137.02001
[2] J.  Jakubík: Affine completeness of complete lattice ordered groups. Czechoslovak Math.  J. 45 (1995), 571–576. MR 1344522
[3] J.  Jakubík: On the affine completeness of lattice ordered groups. Czechoslovak Math.  J. 54 (2004), 423–429. DOI 10.1023/B:CMAJ.0000042381.83544.a7 | MR 2059263
[4] J.  Jakubík and M.  Csontóová: Affine completeness of projectable lattice ordered groups. Czechoslovak Math.  J. 48 (1998), 359–363. DOI 10.1023/A:1022849823068 | MR 1624264
[5] K.  Kaarli and A. F.  Pixley: Polynomial Completeness in Algebraic Systems. Chapman-Hall, London-New York-Washington, 2000. MR 1888967
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