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Algebra Logika, 2016, Volume 55, Number 6, Pages 760–768 (Mi al773)  

This article is cited in 4 scientific papers (total in 4 papers)

Algebraically equivalent clones

A. G. Pinus

Novosibirsk State Technical University, pr. Marksa 20, Novosibirsk, 630092 Russia

Abstract: Two functional clones $F$ and $G$ on a set $A$ are said to be algebraically equivalent if sets of solutions for $F$- and $G$-equations coincide on $A$. It is proved that pairwise algebraically nonequivalent existentially additive clones on finite sets $A$ are finite in number. We come up with results on the structure of algebraic equivalence classes, including an equationally additive clone, in the lattices of all clones on finite sets.

Keywords: clone, equationally additive clone, algebraically equivalent clones, lattice.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 2014/138
Supported by the Russian Ministry of Education and Science (gov. contract 2014/138, project No. 1052).


DOI: https://doi.org/10.17377/alglog.2016.55.605

Full text: PDF file (135 kB)
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English version:
Algebra and Logic, 2017, 55:6, 501–506

Bibliographic databases:

UDC: 512.57
Received: 02.03.2016

Citation: A. G. Pinus, “Algebraically equivalent clones”, Algebra Logika, 55:6 (2016), 760–768; Algebra and Logic, 55:6 (2017), 501–506

Citation in format AMSBIB
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\paper Algebraically equivalent clones
\jour Algebra Logika
\yr 2016
\vol 55
\issue 6
\pages 760--768
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\crossref{https://doi.org/10.17377/alglog.2016.55.605}
\transl
\jour Algebra and Logic
\yr 2017
\vol 55
\issue 6
\pages 501--506
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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. A. G. Pinus, “Algebraic sets of universal algebras and algebraic closure operator”, Lobachevskii J. Math., 38:4, SI (2017), 719–723  crossref  mathscinet  zmath  isi  scopus
    2. A. G. Pinus, “On the logical equivalence of functional clones”, Siberian Math. J., 58:4 (2017), 672–675  mathnet  crossref  crossref  isi  elib  elib
    3. A. G. Pinus, “Ob elementarnoi geometrii universalnykh algebr i ob ekvivalentnosti klonov otnositelno etoi geometrii”, Sib. elektron. matem. izv., 15 (2018), 332–337  mathnet  crossref  mathscinet  zmath
    4. E. Aichinger, B. Rossi, “A clonoid based approach to some finiteness results in universal algebraic geometry”, Algebr. Universalis, 81:1 (2020)  crossref  mathscinet  isi  scopus
  • Алгебра и логика Algebra and Logic
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