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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
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##### References:
 [1] ČERNÁK Š.: On the maximal Dedekind completion of a lattice ordered group. Math. Slovaca 29 (1979), 305-313. · Zbl 0416.06018 [2] EVERETT C. J.: Sequence completion of lattice modules. Duke Math, J. 11 (1944), 109-119. · Zbl 0060.06301 [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 [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
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