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Algebra i logika, 2018, Volume 57, Number 6, Pages 684–710
DOI: https://doi.org/10.33048/alglog.2018.57.604
(Mi al874)
 

This article is cited in 21 scientific papers (total in 21 papers)

Structure of Quasivariety Lattices. I. Independent Axiomatizability

A. V. Kravchenkoabcd, A. M. Nurakunove, M. V. Schwidefskyad

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Siberian Institute of Management — Branch of the Russian Presidental Academy of National Economics and Public Administration, Novosibirsk
c Novosibirsk State Technical University
d Novosibirsk State University
e Institute of Mathematics of the National Academy of Sciences of the Kyrgyz Republic
References:
Abstract: We find a sufficient condition for a quasivariety KK to have continuum many subquasivarieties that have no independent quasi-equational bases relative to KK but have ωω-independent quasi-equational bases relative to KK. This condition also implies that KK is QQ-universal.
Keywords: independent basis, quasi-identity, quasivariety, quasivariety lattice, Q-universality.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation НШ-6848.2016.1
Received: 21.06.2017
Revised: 02.07.2018
English version:
Algebra and Logic, 2019, Volume 57, Issue 6, Pages 445–462
DOI: https://doi.org/10.1007/s10469-019-09516-4
Bibliographic databases:
Document Type: Article
UDC: 512.57
Language: Russian
Citation: A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky, “Structure of Quasivariety Lattices. I. Independent Axiomatizability”, Algebra Logika, 57:6 (2018), 684–710; Algebra and Logic, 57:6 (2019), 445–462
Citation in format AMSBIB
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\by A.~V.~Kravchenko, A.~M.~Nurakunov, M.~V.~Schwidefsky
\paper Structure of Quasivariety Lattices. I. Independent Axiomatizability
\jour Algebra Logika
\yr 2018
\vol 57
\issue 6
\pages 684--710
\mathnet{http://mi.mathnet.ru/al874}
\crossref{https://doi.org/10.33048/alglog.2018.57.604}
\transl
\jour Algebra and Logic
\yr 2019
\vol 57
\issue 6
\pages 445--462
\crossref{https://doi.org/10.1007/s10469-019-09516-4}
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Linking options:
  • https://www.mathnet.ru/eng/al874
  • https://www.mathnet.ru/eng/al/v57/i6/p684
    Cycle of papers
    This publication is cited in the following 21 articles:
    1. M. V. Schwidefsky, “Existence of Independent Quasi-Equational Bases. II”, Algebra Logic, 2024  crossref
    2. A. I. Budkin, “On the independent axiomatizability of quasivarieties of nilpotent groups”, Siberian Math. J., 64:1 (2023), 22–32  mathnet  crossref  crossref  mathscinet
    3. M. V. Schwidefsky, “The complexity of quasivariety lattices. II”, Sib. elektron. matem. izv., 20:1 (2023), 501–513  mathnet  crossref
    4. Anvar M. Nurakunov, Marina V. Schwidefsky, “Profinite Locally Finite Quasivarieties”, Stud Logica, 2023  crossref
    5. M. V. Shvidefski, “O suschestvovanii nezavisimykh bazisov kvazitozhdestv. II”, Algebra i logika, 62:6 (2023), 762–785  mathnet  crossref
    6. A. V. Kravchenko, “On directed and finitely partitionable bases for quasi-identities”, Sib. elektron. matem. izv., 19:2 (2022), 741–746  mathnet  crossref  mathscinet
    7. A. V. Kravchenko, M. V. Schwidefsky, “On nonstandard quasivarieties of differential groupoids and unary algebras”, Sib. elektron. matem. izv., 19:2 (2022), 768–783  mathnet  crossref  mathscinet
    8. Kira Adaricheva, Jennifer Hyndman, J. B. Nation, Joy N. Nishida, CMS/CAIMS Books in Mathematics, 3, A Primer of Subquasivariety Lattices, 2022, 1  crossref
    9. M. E. Adams, W. Dziobiak, H. P. Sankappanavar, “A relatively finite-to-finite universal but not Q-universal quasivariety”, Algebra Univers., 83:3 (2022)  crossref
    10. A. I. Budkin, “Independent axiomatizability of quasivarieties of torsion-free nilpotent groups”, Algebra and Logic, 60:2 (2021), 79–88  mathnet  crossref  crossref  isi
    11. A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky, “Structure of quasivariety lattices. IV. Nonstandard quasivarieties”, Siberian Math. J., 62:5 (2021), 850–858  mathnet  crossref  crossref  isi  elib
    12. V. K. Kartashov, A. V. Kartashova, “Kharakterizatsiya distributivnykh reshetok kvazimnogoobrazii unarov”, Chebyshevskii sb., 22:1 (2021), 177–187  mathnet  crossref
    13. M. V. Schwidefsky, “On a class of subsemigroup lattices”, Siberian Math. J., 61:5 (2020), 941–952  mathnet  crossref  crossref  isi  elib
    14. A. I. Budkin, “On the quasivarieties generated by a finite group and lacking any independent bases of quasi-identities”, Siberian Math. J., 61:6 (2020), 983–993  mathnet  crossref  crossref  isi  elib
    15. A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky, “Structure of quasivariety lattices. III. Finitely partitionable bases”, Algebra and Logic, 59:3 (2020), 222–229  mathnet  crossref  crossref  isi
    16. A. V. Kravchenko, M. V. Schwidefsky, “On the complexity of the lattices of subvarieties and congruences. II. Differential groupoids and unary algebras”, Sib. elektron. matem. izv., 17 (2020), 753–768  mathnet  crossref
    17. M. V. Schwidefsky, “On sufficient conditions for $Q$-universality”, Sib. elektron. matem. izv., 17 (2020), 1043–1051  mathnet  crossref
    18. A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky, “On the Complexity of the Lattices of Subvarieties and Congruences”, Int. J. Algebr. Comput., 30:8 (2020), 1609–1624  crossref  mathscinet  zmath  isi  scopus
    19. A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky, “Structure of quasivariety lattices. II. Undecidable problems”, Algebra and Logic, 58:2 (2019), 123–136  mathnet  crossref  crossref  isi
    20. M. V. Schwidefsky, “Existence of independent quasi-equational bases”, Algebra and Logic, 58:6 (2020), 514–537  mathnet  crossref  crossref  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Алгебра и логика Algebra and Logic
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