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Algebra Logika, 2014, Volume 53, Number 3, Pages 372–400 (Mi al640)  

This article is cited in 5 scientific papers (total in 5 papers)

Quasivariety lattices of pointed Abelian groups

A. M. Nurakunov

Institute of Theoretical and Applied Mathematics, National Academy of Science of the Kyrgyz Republic, pr. Chui 265a, Bishkek, 720071, Kyrgyzstan

Abstract: We give a description of quasicritical pointed Abelian groups. It is proved that the quasivariety lattice of pointed Abelian groups is $Q$-universal. We construct a quasivariety lattice of pointed Abelian groups whose set of finite sublattices is uncomputable. It is shown that there exists a continuum of such lattices of quasivarieties.

Keywords: quasivariety of algebras, pointed Abelian group, congruence, congruence lattice, quasivariety lattice, Birkhoff–Mal'tsev problem, uncomputable set.

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English version:
Algebra and Logic, 2014, 53:3, 238–257

Bibliographic databases:

UDC: 512.57
Received: 28.01.2014
Revised: 23.02.2014

Citation: A. M. Nurakunov, “Quasivariety lattices of pointed Abelian groups”, Algebra Logika, 53:3 (2014), 372–400; Algebra and Logic, 53:3 (2014), 238–257

Citation in format AMSBIB
\Bibitem{Nur14}
\by A.~M.~Nurakunov
\paper Quasivariety lattices of pointed Abelian groups
\jour Algebra Logika
\yr 2014
\vol 53
\issue 3
\pages 372--400
\mathnet{http://mi.mathnet.ru/al640}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3288442}
\transl
\jour Algebra and Logic
\yr 2014
\vol 53
\issue 3
\pages 238--257
\crossref{https://doi.org/10.1007/s10469-014-9286-5}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84922071209}


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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. M. V. Schwidefsky, “Complexity of quasivariety lattices”, Algebra and Logic, 54:3 (2015), 245–257  mathnet  crossref  crossref  mathscinet  isi
    2. S. M. Lutsak, “O slozhnosti reshetok kvazimnogoobrazii”, Sib. elektron. matem. izv., 14 (2017), 92–97  mathnet  crossref
    3. A. Basheyeva, A. Nurakunov, M. Schwidefsky, A. Zamojska-Dzienio, “Lattices of subclasses. III”, Sib. elektron. matem. izv., 14 (2017), 252–263  mathnet  crossref
    4. S. M. Lutsak, “The complexity of quasivariety lattices of unary algebras”, Bull. Karaganda Univ-Math., 85:1 (2017), 65–70  isi
    5. A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky, “Structure of Quasivariety Lattices. I. Independent Axiomatizability”, Algebra and Logic, 57:6 (2019), 445–462  mathnet  crossref  crossref  isi
  • Алгебра и логика Algebra and Logic
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