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Affine completeness and lexicographic product decompositions of abelian lattice ordered groups. (English) Zbl 1081.06022

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.

MSC:

06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
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References:

[1] L. Fuchs: Partially Ordered Algebraic Systems. Pergamon Press, Oxford, 1963. · Zbl 0137.02001
[2] J. Jakubik: Affine completeness of complete lattice ordered groups. Czechoslovak Math. J. 45 (1995), 571–576.
[3] J. Jakubik: On the affine completeness of lattice ordered groups. Czechoslovak Math. J. 54 (2004), 423–429. · Zbl 1080.06027
[4] J. Jakubik and M. Csontoova: Affine completeness of projectable lattice ordered groups. Czechoslovak Math. J. 48 (1998), 359–363. · Zbl 0952.06024
[5] K. Kaarli and A. F. Pixley: Polynomial Completeness in Algebraic Systems. Chapman-Hall, London-New York-Washington, 2000.
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