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Algebra Logika, 2003, Volume 42, Number 1, Pages 26–36 (Mi al15)  

This article is cited in 4 scientific papers (total in 4 papers)

Symmetry of Sections in Fields of Formal Power Series and a Non-Standard Real Line

N. Yu. Galanova

Tomsk State University

Abstract: Let $R[[G,\beta]]$ be a field of formal power series with real coefficients, whose supports are well ordered subsets of an Abelian group $G$ of cardinality strictly less than $\beta$. For $R[[G,\beta]]$, we give criteria of a section being symmetric and of a symmetric section being Dedekind. It is proved that an $\alpha^+$-saturated non-standard real line $^{*}R$ is isomorphic to some field of the form $R[[G,\alpha^+]]$. For $^{*}R$, some consequences are inferred regarding symmetric sections, and the cofinality of “banks” of the sections.

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English version:
Algebra and Logic, 2003, 42:1, 14–19

Bibliographic databases:

UDC: 512.62.52
Received: 06.12.2000
Revised: 29.06.2002

Citation: N. Yu. Galanova, “Symmetry of Sections in Fields of Formal Power Series and a Non-Standard Real Line”, Algebra Logika, 42:1 (2003), 26–36; Algebra and Logic, 42:1 (2003), 14–19

Citation in format AMSBIB
\Bibitem{Gal03}
\by N.~Yu.~Galanova
\paper Symmetry of Sections in Fields of Formal Power Series and a Non-Standard Real Line
\jour Algebra Logika
\yr 2003
\vol 42
\issue 1
\pages 26--36
\mathnet{http://mi.mathnet.ru/al15}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1988021}
\zmath{https://zbmath.org/?q=an:1035.12004}
\transl
\jour Algebra and Logic
\yr 2003
\vol 42
\issue 1
\pages 14--19
\crossref{https://doi.org/10.1023/A:1022672606591}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-42249099316}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. Yu. Galanova, G. G. Pestov, “Symmetry of cuts in fields of formal power series”, Algebra and Logic, 47:2 (2008), 100–106  mathnet  crossref  mathscinet  zmath  isi
    2. G. G. Pestov, “Issledovaniya po uporyadochennym gruppam i polyam v Tomskom gosudarstvennom universitete”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2011, no. 3(15), 41–58  mathnet  elib
    3. N. Yu. Galanova, “Lineino uporyadochennye polya s simmetrichnymi secheniyami”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2017, no. 46, 14–20  mathnet  crossref  elib
    4. N. Yu. Galanova, “O simmetrichnykh secheniyakh odnogo veschestvenno zamknutogo polya”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2018, no. 53, 5–15  mathnet  crossref  elib
  • Алгебра и логика Algebra and Logic
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