Irreducibility and Multiplicative Composition of Polynomials Over Finite Fields

Benferhat, Leila; Kihel, Omar; Larone, Jesse; Mohamed, Rezki Ould

doi:10.2478/tmmp-2023-0001

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Irreducibility and Multiplicative Composition of Polynomials Over Finite Fields

Tatra Mountains Mathematical Publications

Volume 83 (2023): Issue 1 (February 2023)

By: Leila Benferhat, Omar Kihel, Jesse Larone and Rezki Ould Mohamed

Open Access

|Mar 2023

Abstract

The aim of this paper is to provide integral polynomials irreducible over ℤ which are reducible over 𝔽_p for every prime p. In particular, we show that certain composed products of integral polynomials are reducible modulo p for all primes p.

References

[1] AYAD, M.: On irreducible polynomials over Q which are reducible over 𝔽_p for all p, Rocky Mountain J. Math. 40 (2010), no. 5, 1377–1389.10.1216/RMJ-2010-40-5-1377
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[2] BENFERHAT, L.—BENOUMHANI, S. M.—BOUMAHDI, R.— LARONE, J.: Additive decompositions of polynomials over unique factorization domains, J. Algebra Appl, 19 (2020), no. 8, 1–11.10.1142/S0219498820501509
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[3] BRAWLEY, J. V.—CARLITZ, L.: Irreducibles and the composed product for polynomials over a finite field, Discrete Math. 65 (1987), no. 2, 115–139.10.1016/0012-365X(87)90135-X
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DOI: https://doi.org/10.2478/tmmp-2023-0001 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195

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Language: English

Page range: 1 - 10

Submitted on: Nov 8, 2022

Published on: Mar 7, 2023

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

polynomial,

polynomial decomposition,

resultant

Related subjects:

Mathematics,

General mathematics

© 2023 Leila Benferhat, Omar Kihel, Jesse Larone, Rezki Ould Mohamed, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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