×

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
PDFBibTeX XMLCite
Full Text: DOI EuDML Link

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.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.