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The Largest Group Contained in the Order Completion of a Totally Ordered Group

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Abstract

For a totally ordered group G we determine the largest group contained in its Dedekind completion G#. It was the result of studying the family of convex subgroups of G and some well-known properties of ordered groups.

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References

  1. A. H. Clifford, “Note on Hahn’s theorem on ordered abelian groups,” Proc. Amer. Math. Soc. 5 (6), 860–863 (1954).

    MathSciNet  MATH  Google Scholar 

  2. A. B. Comicheo, “Generalized open mapping theorem for x-normed spaces,” p-Adic Numbers Ultrametric Anal. Appl. 11 (2), 135–150 (2019).

    Article  MathSciNet  Google Scholar 

  3. L. Fuchs, Partially Ordered Algebraic Systems, (Pergamon Press, Oxford-London-New York-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass.-Palo Alto, Calif.-London, 1963).

    MATH  Google Scholar 

  4. H. Ochsenius, E. Olivos and C. Perez-Garcia, “Wim Schikhof: our colleague and friend,” in Advances in Non-Archimedean Analysis, Contemp. Math. 665, 199–249 (Amer. Math. Soc., Providence, RI, 2016).

    MathSciNet  MATH  Google Scholar 

  5. H. Ochsenius and W. H. Schikhof, “Banach spaces over fields with an infinite rank valuation,” in p-Adic Functional Analysis (Poznań 1998), Lect. Notes Pure Appl. Math. 207, 233–293 (Dekker, New York, 1999).

    MathSciNet  MATH  Google Scholar 

  6. H. Ochsenius and W. H. Schikhof, “Lipschitz operators on Banach spaces over Krull valued fields,” in Ultrametric Functional Analysis, Contemp. Math. 384, 203–233 (Amer. Math. Soc., Providence, RI, 2005).

    Article  MathSciNet  Google Scholar 

  7. E. Olivos and W. H. Schikhof, “Extending the multiplication of a totally ordered group to its completion,” in Advances in Non-Archimedean Analysis, Contemp. Math. 551, 231–242 (Amer. Math. Soc., Providence, RI, 2011).

    Article  MathSciNet  Google Scholar 

  8. E. Olivos and W. H. Schikhof, “Algebra and topology on the Dedekind completion of a totally ordered abelian group,” Indag. Math. (N.S.) 24 (1), 291–304 (2013).

    Article  MathSciNet  Google Scholar 

  9. K. Shamseddine, “Analysis on the Levi-Civita field and computational applications,” Appl. Math. Comput. 255, 44–57 (2015).

    MathSciNet  MATH  Google Scholar 

  10. F. J. Ugarte, “Estructura de los grupos abelianos ordenados,” Pro Math. 29 (57), 105–128 (2016).

    Google Scholar 

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Correspondence to Adrialy Muci or Elena Olivos.

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The text was submitted by the authors in English.

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Muci, A., Olivos, E. The Largest Group Contained in the Order Completion of a Totally Ordered Group. P-Adic Num Ultrametr Anal Appl 12, 123–133 (2020). https://doi.org/10.1134/S2070046620020041

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  • DOI: https://doi.org/10.1134/S2070046620020041

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