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Algebra Logika, 2005, Volume 44, Number 5, Pages 540–559 (Mi al130)  

This article is cited in 1 scientific paper (total in 1 paper)

Elementary Theory for $l$-Ideal Lattices of Abelian $l$-Groups

N. Ya. Medvedev


Abstract: A description is furnished for ideal lattices of free vector lattices $\mathcal F_n$ with a finite number $n$ of free generators. It is proved that an elementary theory for $l$-ideal lattices of Abelian lattice-ordered groups is undecidable, which gives a negative solution to Problem 5.20 in the “Kourovka Notebook.”

Keywords: free vector lattice, ideal lattice, elementary theory

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English version:
Algebra and Logic, 2005, 44:5, 302–312

Bibliographic databases:

UDC: 512.545
Received: 02.06.2004

Citation: N. Ya. Medvedev, “Elementary Theory for $l$-Ideal Lattices of Abelian $l$-Groups”, Algebra Logika, 44:5 (2005), 540–559; Algebra and Logic, 44:5 (2005), 302–312

Citation in format AMSBIB
\Bibitem{Med05}
\by N.~Ya.~Medvedev
\paper Elementary Theory for $l$-Ideal Lattices of Abelian $l$-Groups
\jour Algebra Logika
\yr 2005
\vol 44
\issue 5
\pages 540--559
\mathnet{http://mi.mathnet.ru/al130}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2195019}
\zmath{https://zbmath.org/?q=an:1101.06012}
\transl
\jour Algebra and Logic
\yr 2005
\vol 44
\issue 5
\pages 302--312
\crossref{https://doi.org/10.1007/s10469-005-0029-5}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-27544512131}


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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. O. A. Kuryleva, “Interpreting arithmetics in the ideal lattice of a free vector lattice $\mathcal F_n$”, Algebra and Logic, 47:1 (2008), 42–48  mathnet  crossref  mathscinet  zmath  isi
  • Алгебра и логика Algebra and Logic
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