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# Article

 Title: Distinguished completion of a direct product of lattice ordered groups (English) Author: Jakubík, Ján Language: English Journal: Czechoslovak Mathematical Journal ISSN: 0011-4642 (print) ISSN: 1572-9141 (online) Volume: 51 Issue: 3 Year: 2001 Pages: 661-671 Summary lang: English . Category: math . Summary: 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]. (English) Keyword: lattice ordered group Keyword: distinguished completion Keyword: direct product MSC: 06F15 idZBL: Zbl 1079.06505 idMR: MR1851554 . Date available: 2009-09-24T10:46:04Z Last updated: 2020-07-03 Stable URL: http://hdl.handle.net/10338.dmlcz/127676 . Reference: [1] R. N.  Ball: The distinguished completion of a lattice ordered group.In: Algebra Carbondale 1980, Lecture Notes Math. 848, Springer Verlag, 1980, pp. 208–217. MR 0613187 Reference: [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 1036072 Reference: [3] R. N. Ball: Distinguished extensions of a lattice ordered group.Algebra Univ. 35 (1996), 85–112. Zbl 0842.06012, MR 1360533, 10.1007/BF01190971 Reference: [4] P.  Conrad: Lattice Ordered Groups.Tulane University, 1970. Zbl 0258.06011 Reference: [5] J.  Jakubík: Generalized Dedekind completion of a lattice ordered group.Czechoslovak Math. J. 28 (1978), 294–311. MR 0552650 Reference: [6] J.  Jakubík: Maximal Dedekind completion of an abelian lattice ordered group.Czechoslovak Math. J. 28 (1978), 611–631. MR 0506435 Reference: [7] J. Jakubík: Distinguished extensions of an $MV$-algebra.Czechoslovak Math. J. 49 (1999), 867–876. MR 1746712, 10.1023/A:1022469521480 .

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