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Algebra Logika, 2003, Volume 42, Number 2, Pages 237–254 (Mi al28)  

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

Varieties Defined by Permutations

D. M. Smirnov


Abstract: We continue to study interrelations between permutative varieties and the cyclic varieties defined by cycles of the form $(1 2\ldots k)$. A criterion is given determining whether a cyclic variety $G_k$ is interpretable in $ _nG_\pi$. For a permutation $\pi$ without fixed elements, it is stated that a set of primes $p$ for which $ _nG_\pi$ is interpretable in $G_p$ in the lattice $\mathbb L^int$ is finite. It is also proved that for distinct primes $p_1,\ldots,p_r$, the Helly number of a type $[G_{p_1}]\wedge\ldots\wedge[G_{p_r}]$ in $\mathbb L^int$ coincides with dimension of the dual type $[G_{p_1}]\vee\ldots\vee[G_{p_r}]$ and equals $r$.

Keywords: permutative variety, cyclic variety, interpretable variety, Helly number.

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English version:
Algebra and Logic, 2003, 42:2, 136–146

Bibliographic databases:

UDC: 512.572
Received: 17.02.2001

Citation: D. M. Smirnov, “Varieties Defined by Permutations”, Algebra Logika, 42:2 (2003), 237–254; Algebra and Logic, 42:2 (2003), 136–146

Citation in format AMSBIB
\Bibitem{Smi03}
\by D.~M.~Smirnov
\paper Varieties Defined by Permutations
\jour Algebra Logika
\yr 2003
\vol 42
\issue 2
\pages 237--254
\mathnet{http://mi.mathnet.ru/al28}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2003632}
\zmath{https://zbmath.org/?q=an:1030.08001}
\transl
\jour Algebra and Logic
\yr 2003
\vol 42
\issue 2
\pages 136--146
\crossref{https://doi.org/10.1023/A:1023358508796}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-18244370617}


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

    This publication is cited in the following articles:
    1. D. M. Smirnov, “Interpretability Types for Regular Varieties of Algebras”, Algebra and Logic, 43:2 (2004), 128–131  mathnet  crossref  mathscinet  zmath
    2. D. M. Smirnov, “Lattices of Interpretability Types of Varieties”, Algebra and Logic, 44:2 (2005), 109–116  mathnet  crossref  mathscinet  zmath
    3. D. M. Smirnov, “Arithmetic Interpretability Types of Varieties and Some Additive Problems with Primes”, Algebra and Logic, 44:5 (2005), 348–352  mathnet  crossref  mathscinet  zmath
  • Алгебра и логика Algebra and Logic
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