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

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Diskretnaya Matematika, 2017, Volume 29, Issue 3, Pages 54–69
DOI: https://doi.org/10.4213/dm1452 (Mi dm1452)

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

Closed classes of polynomials modulo

p^{2}

$p^2$

D. G. Meshchaninov

National Research University "Moscow Power Engineering Institute"

Full-text PDF (1225 kB) Citations (4)

References:

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

Abstract: We consider functions of

p^{2}

$p^2$ -valued logic (

p

$p$ 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.

Received: 05.05.2017

English version:
Discrete Mathematics and Applications, 2018, Volume 28, Issue 3, Pages 167–178
DOI: https://doi.org/10.1515/dma-2018-0016

Bibliographic databases:

UDC: 519.716

Language: Russian

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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\jour Discrete Math. Appl.

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\pages 167--178

\crossref{https://doi.org/10.1515/dma-2018-0016}

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Linking options:

https://www.mathnet.ru/eng/dm1452

https://doi.org/10.4213/dm1452

https://www.mathnet.ru/eng/dm/v29/i3/p54

This publication is cited in the following 4 articles:

S. N. Selezneva, “Opisanie zamknutogo klassa polinomialnykh funktsii po modulyu stepeni prostogo chisla posredstvom otnosheniya”, Diskret. matem., 35:4 (2023), 115–125
D. G. Meschaninov, “Peresecheniya klassov $k$ -znachnykh funktsii, sokhranyayuschikh sravneniya i raznosti”, Material konferentsii: “XIV mezhdunarodnyi nauchnyi seminar "Diskretnaya matematika i ee prilozheniya” imeni akademika O.B. Lupanova (20-25 iyunya 2022 g., Moskva), 2022, 133
D. G. Meshchaninov, “Some families of closed classes in $P_k$ defined by additive formulas”, Discrete Math. Appl., 32:2 (2022), 115–128
D. G. Meshchaninov, “A Family of Closed Classes in k-Valued Logic”, Moscow Univ. Comput. Math. Cybern., 43:1 (2019), 25

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

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Abstract page:	482
Full-text PDF :	104
References:	84
First page:	42

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