Abstract:
The closed class $\operatorname{Pol}_{p^m}$ in $p^m$-valued logic, where $p$ is a prime number, $1 \leqslant m \leqslant p$, is studied. This class consists of all functions that are polynomial modulo $p^m$. Criteria for polynomiality modulo $p^m$ of a function in $p^m$-valued logic are found. A relation describing the class $\operatorname{Pol}_{p^m}$ is obtained in an explicit form.
Keywords:
function of many-valued logic, residue ring, polynomial, closed class, relation.
The work is supported by the Ministry of Education and Science of the Russian Federation as a part of the program for the Moscow Center for Fundamental and Applied Mathematics, project no. 075-15-2022-284.
Citation:
S. N. Selezneva, “Describing the closed class of polynomial functions modulo a power of a prime number by a relation”, Diskr. Mat., 35:4 (2023), 115–125; Discrete Math. Appl., 35:2 (2025), 125–133
\Bibitem{Sel23}
\by S.~N.~Selezneva
\paper Describing the closed class of polynomial functions modulo a power of a prime number by a relation
\jour Diskr. Mat.
\yr 2023
\vol 35
\issue 4
\pages 115--125
\mathnet{http://mi.mathnet.ru/dm1803}
\crossref{https://doi.org/10.4213/dm1803}
\transl
\jour Discrete Math. Appl.
\yr 2025
\vol 35
\issue 2
\pages 125--133
\crossref{https://doi.org/10.1515/dma-2025-0008}
Linking options:
https://www.mathnet.ru/eng/dm1803
https://doi.org/10.4213/dm1803
https://www.mathnet.ru/eng/dm/v35/i4/p115
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