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Distinguished completion of a direct product of lattice ordered groups. (English) Zbl 1079.06505
Summary: In the present paper we prove that if a lattice ordered group \(G\) is a direct product of lattice ordered groups \(G_i\) \((i\in I)\), then \(E(G)\) is a direct product of the lattice ordered groups \(E(G_i)\).
From this we obtain a generalization of a result of R. N. Ball [Algebra Univers. 35, 85-112 (1996; Zbl 0842.06012)].
MSC:
06F15 Ordered groups
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References:
[1] R. N. Ball: The distinguished completion of a lattice ordered group. Algebra Carbondale 1980, Lecture Notes Math. 848, Springer Verlag, 1980, pp. 208-217.
[2] R. N. Ball: Completions of \(\ell \)-groups. Lattice Ordered Groups, A. M. W. Glass and W. C. Holland (eds.), Kluwer, Dordrecht-Boston-London, 1989, pp. 142-177.
[3] R. N. Ball: Distinguished extensions of a lattice ordered group. Algebra Univ. 35 (1996), 85-112. · Zbl 0842.06012
[4] P. Conrad: Lattice Ordered Groups. Tulane University, 1970. · Zbl 0258.06011
[5] J. Jakubík: Generalized Dedekind completion of a lattice ordered group. Czechoslovak Math. J. 28 (1978), 294-311. · Zbl 0391.06013
[6] J. Jakubík: Maximal Dedekind completion of an abelian lattice ordered group. Czechoslovak Math. J. 28 (1978), 611-631. · Zbl 0432.06012
[7] J. Jakubík: Distinguished extensions of an \(MV\)-algebra. Czechoslovak Math. J. 49 (1999), 867-876. · Zbl 1004.06012
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