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

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

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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
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\crossref{https://doi.org/10.4213/dm1452}
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\jour Discrete Math. Appl.
\yr 2018
\vol 28
\issue 3
\pages 167--178
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