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

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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. Kravchenko^abcd, A. M. Nurakunov^e, M. V. Schwidefsky^ad

^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

Full-text PDF (326 kB) Citations (21)

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DOI: https://doi.org/10.33048/alglog.2018.57.604

Abstract: We find a sufficient condition for a quasivariety

K

$\mathbf{K}$ to have continuum many subquasivarieties that have no independent quasi-equational bases relative to

K

$\mathbf{K}$ but have

ω

$\omega$ -independent quasi-equational bases relative to

K

$\mathbf{K}$ . This condition also implies that

K

$\mathbf{K}$ is

Q

$Q$ -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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\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

Structure of Quasivariety Lattices. I. Independent Axiomatizability
A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky
Algebra Logika, 2018, 57:6, 684–710
Structure of quasivariety lattices. II. Undecidable problems
A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky
Algebra Logika, 2019, 58:2, 179–199
Structure of quasivariety lattices. III. Finitely partitionable bases
A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky
Algebra Logika, 2020, 59:3, 323–333
Structure of quasivariety lattices. IV. Nonstandard quasivarieties
A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky
Sibirsk. Mat. Zh., 2021, 62:5, 1049–1060

This publication is cited in the following 21 articles:

M. V. Schwidefsky, “Existence of Independent Quasi-Equational Bases. II”, Algebra Logic, 2024
A. I. Budkin, “On the independent axiomatizability of quasivarieties of nilpotent groups”, Siberian Math. J., 64:1 (2023), 22–32
M. V. Schwidefsky, “The complexity of quasivariety lattices. II”, Sib. elektron. matem. izv., 20:1 (2023), 501–513
Anvar M. Nurakunov, Marina V. Schwidefsky, “Profinite Locally Finite Quasivarieties”, Stud Logica, 2023
M. V. Shvidefski, “O suschestvovanii nezavisimykh bazisov kvazitozhdestv. II”, Algebra i logika, 62:6 (2023), 762–785
A. V. Kravchenko, “On directed and finitely partitionable bases for quasi-identities”, Sib. elektron. matem. izv., 19:2 (2022), 741–746
A. V. Kravchenko, M. V. Schwidefsky, “On nonstandard quasivarieties of differential groupoids and unary algebras”, Sib. elektron. matem. izv., 19:2 (2022), 768–783
Kira Adaricheva, Jennifer Hyndman, J. B. Nation, Joy N. Nishida, CMS/CAIMS Books in Mathematics, 3, A Primer of Subquasivariety Lattices, 2022, 1
M. E. Adams, W. Dziobiak, H. P. Sankappanavar, “A relatively finite-to-finite universal but not Q-universal quasivariety”, Algebra Univers., 83:3 (2022)
A. I. Budkin, “Independent axiomatizability of quasivarieties of torsion-free nilpotent groups”, Algebra and Logic, 60:2 (2021), 79–88
A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky, “Structure of quasivariety lattices. IV. Nonstandard quasivarieties”, Siberian Math. J., 62:5 (2021), 850–858
V. K. Kartashov, A. V. Kartashova, “Kharakterizatsiya distributivnykh reshetok kvazimnogoobrazii unarov”, Chebyshevskii sb., 22:1 (2021), 177–187
M. V. Schwidefsky, “On a class of subsemigroup lattices”, Siberian Math. J., 61:5 (2020), 941–952
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
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
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
M. V. Schwidefsky, “On sufficient conditions for $Q$ -universality”, Sib. elektron. matem. izv., 17 (2020), 1043–1051
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
A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky, “Structure of quasivariety lattices. II. Undecidable problems”, Algebra and Logic, 58:2 (2019), 123–136
M. V. Schwidefsky, “Existence of independent quasi-equational bases”, Algebra and Logic, 58:6 (2020), 514–537

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

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