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Diskr. Mat., 2015, Volume 27, Issue 4, Pages 79–93 (Mi dm1349)  

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

Galois theory for clones and superclones

N. A. Peryazeva, I. K. Sharankhaevb

a Saint Petersburg Electrotechnical University "LETI"
b Buryat State University

Abstract: We study clones (closed sets of operations that contain projections) and superclones on finite sets. According to A. I. Mal'tsev a clone may be considered as an algebra. If we replace algebra universe with a set of multioperations and add the operation of simplest equation solvability then we will obtain an algebra called a superclone. The paper establishes Galois connection between clones and superclones.

Keywords: clone, superclone, operation, multioperation, superposition

Funding Agency Grant Number
Russian Foundation for Basic Research 12-01-000351a
Research was supported by RFBR, project number 12-01-000351a.


DOI: https://doi.org/10.4213/dm1349

Full text: PDF file (461 kB)
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English version:
Discrete Mathematics and Applications, 2016, 26:4, 227–238

Bibliographic databases:

Document Type: Article
UDC: 519.7
Received: 20.06.2015

Citation: N. A. Peryazev, I. K. Sharankhaev, “Galois theory for clones and superclones”, Diskr. Mat., 27:4 (2015), 79–93; Discrete Math. Appl., 26:4 (2016), 227–238

Citation in format AMSBIB
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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. Nikolay A. Peryazev, Yulia V. Peryazeva, Ivan K. Sharankhaev, “Minimal algebras of unary multioperations”, Zhurn. SFU. Ser. Matem. i fiz., 9:2 (2016), 220–224  mathnet  crossref
    2. A. S. Kazimirov, “O slozhnosti standartnykh form multifunktsii”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 22 (2017), 63–70  mathnet  crossref
    3. N. A. Peryazev, I. K. Sharankhaev, “On some sufficient condition for the equality of multi-clone and super-clone”, Zhurn. SFU. Ser. Matem. i fiz., 11:1 (2018), 97–102  mathnet  crossref
  • Дискретная математика
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