×

zbMATH — the first resource for mathematics

On the maximal Dedekind completion of a half partially ordered group. (English) Zbl 0888.06009
The notion of maximal Dedekind completion is extended to the case of a half partially ordered group. The main result is formulated as follows: Let \(G\) be a half lattice ordered group (half linearly ordered group). Then the maximal Dedekind completion \(M_h(G)\) of \(G\) is a half lattice ordered group (half linearly ordered group).

MSC:
06F15 Ordered groups
PDF BibTeX XML Cite
Full Text: EuDML
References:
[1] ČERNÁK Š.: On the maximal Dedekind completion of a lattice ordered group. Math. Slovaca 29 (1979), 305-313. · Zbl 0416.06018 · eudml:34065
[2] EVERETT C. J.: Sequence completion of lattice modules. Duke Math, J. 11 (1944), 109-119. · Zbl 0060.06301 · doi:10.1215/S0012-7094-44-01112-9
[3] FUCHS L.: Partially Ordered Algebraic Systems. Pergamon Press, Oxford-London-New York-Paris, 1963. · Zbl 0137.02001
[4] GIRAUDET M.-LUCAS F.: Groupes á moitié ordonnés. Fund. Math. 139 (1991). 75-89. · Zbl 0766.06014 · eudml:211895
[5] KOKORIN A. J.-KOPYTOV V. M.: Linearly Ordered Groups. Nauka, Moskva. 1972.
[6] MacNEILLE H. M.: Partially ordered sets. Trans. Amer. Math. Soc. 42 (1937), 416-460. · Zbl 0017.33904 · doi:10.2307/1989739
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.