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Algebra i logika, 2019, Volume 58, Number 3, Pages 320–333
DOI: https://doi.org/10.33048/alglog.2019.58.302
(Mi al897)
 

This article is cited in 3 scientific papers (total in 3 papers)

ω-Independent bases for quasivarieites of torsion-free groups

A. I. Budkin

Altai State University, Barnaul
Full-text PDF (220 kB) Citations (3)
References:
Abstract: It is proved that there exists a set R of quasivarieties of torsion-free groups which (a) have an ω-independent basis of quasi-identities in the class K0 of torsion-free groups, (b) do not have an independent basis of quasi-identities in K0, and (c) the intersection of all quasivarieties in R has an independent quasi-identity basis in K0. The collection of such sets R has the cardinality of the continuum.
Keywords: quasivariety, quasi-identity, independent basis, ω-independent basis, torsion-free group.
Received: 19.04.2018
Revised: 24.09.2019
English version:
Algebra and Logic, 2019, Volume 58, Issue 3, Pages 214–223
DOI: https://doi.org/10.1007/s10469-019-09539-x
Bibliographic databases:
Document Type: Article
UDC: 512.57
Language: Russian
Citation: A. I. Budkin, “ω-Independent bases for quasivarieites of torsion-free groups”, Algebra Logika, 58:3 (2019), 320–333; Algebra and Logic, 58:3 (2019), 214–223
Citation in format AMSBIB
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\by A.~I.~Budkin
\paper $\omega$-Independent bases for quasivarieites
of torsion-free groups
\jour Algebra Logika
\yr 2019
\vol 58
\issue 3
\pages 320--333
\mathnet{http://mi.mathnet.ru/al897}
\crossref{https://doi.org/10.33048/alglog.2019.58.302}
\transl
\jour Algebra and Logic
\yr 2019
\vol 58
\issue 3
\pages 214--223
\crossref{https://doi.org/10.1007/s10469-019-09539-x}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000494787600010}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85074831445}
Linking options:
  • https://www.mathnet.ru/eng/al897
  • https://www.mathnet.ru/eng/al/v58/i3/p320
  • This publication is cited in the following 3 articles:
    1. 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
    2. 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
    3. M. V. Schwidefsky, “On sufficient conditions for $Q$-universality”, Sib. elektron. matem. izv., 17 (2020), 1043–1051  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Алгебра и логика Algebra and Logic
    Statistics & downloads:
    Abstract page:323
    Full-text PDF :33
    References:43
    First page:4
     
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