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Algebra 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

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.

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English version:
Algebra and Logic, 2011, 50:4, 357–364

Bibliographic databases:

UDC: 512.577
Received: 30.11.2010
Revised: 14.02.2011

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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\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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. Basheyeva, A. Nurakunov, M. Schwidefsky, A. Zamojska-Dzienio, “Lattices of subclasses. III”, Sib. elektron. matem. izv., 14 (2017), 252–263  mathnet  crossref
    2. A. O. Basheeva, A. V. Yakovlev, “Ob $\omega$-nezavisimykh bazisakh kvazitozhdestv”, Sib. elektron. matem. izv., 14 (2017), 838–847  mathnet  crossref
    3. A. V. Kravchenko, A. V. Yakovlev, “Quasivarieties of graphs and independent axiomatizability”, Siberian Adv. Math., 28:1 (2018), 53–59  mathnet  crossref  crossref  elib
    4. 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
    5. A. I. Budkin, “Ob $\omega $-nezavisimosti kvazimnogoobrazii nilpotentnykh grupp”, Sib. elektron. matem. izv., 16 (2019), 516–522  mathnet  crossref
    6. A. I. Budkin, “Ob $\omega$-nezavisimykh bazisakh kvazimnogoobrazii grupp bez krucheniya”, Algebra i logika, 58:3 (2019), 320–333  mathnet  crossref
  • Алгебра и логика Algebra and Logic
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