Geodesic
Distinguished completion of a direct product of lattice ordered groups
Czechoslovak Mathematical Journal, Tome 51 (2001) no. 3, pp. 661-671 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The distinguished completion $E(G)$ of a lattice ordered group $G$ was investigated by Ball [1], [2], [3]. An analogous notion for $MV$-algebras was dealt with by the author [7]. 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 Ball [3].
The distinguished completion $E(G)$ of a lattice ordered group $G$ was investigated by Ball [1], [2], [3]. An analogous notion for $MV$-algebras was dealt with by the author [7]. 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 Ball [3].
Classification : 06F15
Keywords: lattice ordered group; distinguished completion; direct product 
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Jakubík, Ján. Distinguished completion of a direct product of lattice ordered groups. Czechoslovak Mathematical Journal, Tome 51 (2001) no. 3, pp. 661-671. http://geodesic.mathdoc.fr/item/CMJ_2001_51_3_a15/

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[2] R. N. Ball: Completions of $\ell $-groups. In: Lattice Ordered Groups, A. M. W.  Glass and W. C. Holland (eds.), Kluwer, Dordrecht-Boston-London, 1989, pp. 142–177. | MR

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[4] P.  Conrad: Lattice Ordered Groups. Tulane University, 1970. | Zbl

[5] J.  Jakubík: Generalized Dedekind completion of a lattice ordered group. Czechoslovak Math. J. 28 (1978), 294–311. | MR

[6] J.  Jakubík: Maximal Dedekind completion of an abelian lattice ordered group. Czechoslovak Math. J. 28 (1978), 611–631. | MR

[7] J. Jakubík: Distinguished extensions of an $MV$-algebra. Czechoslovak Math. J. 49 (1999), 867–876. | DOI | MR