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Diskr. Mat., 2017, Volume 29, Issue 3, Pages 54–69 (Mi dm1452)  

This article is cited in 1 scientific paper (total in 1 paper)

Closed classes of polynomials modulo $p^2$

D. G. Meshchaninov

National Research University "Moscow Power Engineering Institute"

Abstract: We consider functions of $p^2$-valued logic ($p$ is prime) that may be implemented by polynomials over the ring ${\mathbb Z}_{p^2}$, and describe all closed classes that contain linear functions. It turns out that the set of these classes is countable. We also construct the lattice of such classes with respect to inclusion.

Keywords: $k$-valued logic, closed class, clone, polynomials over a ring of residues, lattice of closed classes.

DOI: https://doi.org/10.4213/dm1452

Full text: PDF file (1225 kB)
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English version:
Discrete Mathematics and Applications, 2018, 28:3, 167–178

Bibliographic databases:

UDC: 519.716
Received: 05.05.2017

Citation: D. G. Meshchaninov, “Closed classes of polynomials modulo $p^2$”, Diskr. Mat., 29:3 (2017), 54–69; Discrete Math. Appl., 28:3 (2018), 167–178

Citation in format AMSBIB
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\by D.~G.~Meshchaninov
\paper Closed classes of polynomials modulo $p^2$
\jour Diskr. Mat.
\yr 2017
\vol 29
\issue 3
\pages 54--69
\mathnet{http://mi.mathnet.ru/dm1452}
\crossref{https://doi.org/10.4213/dm1452}
\elib{https://elibrary.ru/item.asp?id=29887802}
\transl
\jour Discrete Math. Appl.
\yr 2018
\vol 28
\issue 3
\pages 167--178
\crossref{https://doi.org/10.1515/dma-2018-0016}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000435373700003}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85048853206}


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  • https://doi.org/10.4213/dm1452
  • http://mi.mathnet.ru/eng/dm/v29/i3/p54

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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. G. Meschaninov, “Nekotorye semeistva zamknutykh klassov v $P_k$, zadavaemykh additivnymi formulami”, Diskret. matem., 33:2 (2021), 100–116  mathnet  crossref
  • Дискретная математика
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