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Algebra i logika, 2011, Volume 50, Number 4, Pages 521–532 (Mi al499)  
This article is cited in 6 scientific papers (total in 6 papers)

Antivarieties of unars

A. V. Kartashova

Volgograd, Russia
Full-text PDF (174 kB) Citations (6)
References:
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Abstract: A complete description of the lattice of all antivarieties of unars is given. It is stated that there exist continuum many antivarieties of unars not having an independent basis of identities and a necessary and sufficient condition is specified under which a finite unar has an independent or finite basis of antiidentities. In addition, it is proved that the lattice of all antivarieties of unars is isomorphic to a lattice of $\mathcal A_{1,1}$-antivarieties, where $\mathcal A_{1,1}$ is a variety of unary algebras of a signature $\langle f,g\rangle$ defined by identities $f(g(x))=g(f(x))=x$.
Keywords: antivariety of unars, lattice, identity.
Received: 30.11.2010
Revised: 14.02.2011
English version:
Algebra and Logic, 2011, Volume 50, Issue 4, Pages 357–364
DOI: https://doi.org/10.1007/s10469-011-9147-4
Bibliographic databases:
Document Type: Article
UDC: 512.577
Language: Russian
Citation: A. V. Kartashova, “Antivarieties of unars”, Algebra Logika, 50:4 (2011), 521–532; Algebra and Logic, 50:4 (2011), 357–364
Citation in format AMSBIB
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\by A.~V.~Kartashova
\paper Antivarieties of unars
\jour Algebra Logika
\yr 2011
\vol 50
\issue 4
\pages 521--532
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2893586}
\zmath{https://zbmath.org/?q=an:1268.08001}
\transl
\jour Algebra and Logic
\yr 2011
\vol 50
\issue 4
\pages 357--364
\crossref{https://doi.org/10.1007/s10469-011-9147-4}
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  • https://www.mathnet.ru/eng/al499
  • https://www.mathnet.ru/eng/al/v50/i4/p521
    • This publication is cited in the following 6 articles:
    1. A. I. Budkin, “Ob $\omega $-nezavisimosti kvazimnogoobrazii nilpotentnykh grupp”, Sib. elektron. matem. izv., 16 (2019), 516–522  mathnet  crossref
    2. A. I. Budkin, “$\omega$-Independent bases for quasivarieites of torsion-free groups”, Algebra and Logic, 58:3 (2019), 214–223  mathnet  crossref  crossref  isi
    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. A. O. Basheeva, A. V. Yakovlev, “Ob $\omega$-nezavisimykh bazisakh kvazitozhdestv”, Sib. elektron. matem. izv., 14 (2017), 838–847  mathnet  crossref
    5. A. V. Kravchenko, A. V. Yakovlev, “Quasivarieties of graphs and independent axiomatizability”, Siberian Adv. Math., 28:1 (2018), 53–59  mathnet  crossref  crossref  elib
    6. A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky, “On quasi-equational bases for differential groupoids and unary algebras”, Sib. elektron. matem. izv., 14 (2017), 1330–1337  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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    		Алгебра и логика Algebra and Logic
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    Abstract page:267
    Full-text PDF :75
    References:62
    First page:6
     
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