On the classification of ideals over $R[X]/\langle f(X)^{p^{s}}\rangle $ when $R=\mathbb {F}_{p^{m}}+u\mathbb {F}_{p^{m}}+\ldots +u^{n}\mathbb {F}

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On the classification of ideals over $R[X]/\langle f(X)^{p^{s}}\rangle $ when $R=\mathbb {F}_{p^{m}}+u\mathbb {F}_{p^{m}}+\ldots +u^{n}\mathbb {F}_{p^{m}}$

Published:2022-12-17 Issue:3 Volume:15 Page:589-598
ISSN:1936-2447
Container-title:Cryptography and Communications
language:en
Short-container-title:Cryptogr. Commun.

Author:

Boudine Brahim^ORCID,Laaouine Jamal,Charkani Mohammed Elhassani

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Computational Theory and Mathematics,Computer Networks and Communications

Link

https://link.springer.com/content/pdf/10.1007/s12095-022-00620-4.pdf

Reference23 articles.

1. Arnold, A., Monagan, M.: Calculating cyclotomic polynomials. Math. Comput. 80(276), 2359–2379 (2011)

2. Atiyah, M.: Introduction to commutative algebra, CRC Press (2018)

3. Brown, W.C.: Matrices Over Commutative Rings. Marcel Dekker Inc., New York (1993)

4. Cao, Y.: Generalized quasi-cyclic codes over Galois rings: structural properties and enumeration, Applicable Algebra in Engineering. Communication and Computing 22(3), 219–233 (2011)

5. Charkani, M.E., Boudine, B.: On the integral ideals of R[X] when R is a special principal ideal ring, Sao Paulo. J. Math. Sci. 14(2), 698–702 (2020)

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