Some Remarks Regarding Special Elements in Algebras Obtained by the Cayley–Dickson Process over Zp

Flaut, Cristina; Baias, Andreea

doi:10.3390/axioms13060351

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Some Remarks Regarding Special Elements in Algebras Obtained by the Cayley–Dickson Process over Z_p

by

Cristina Flaut

^1,*,† and

Andreea Baias

^2,†

¹

Faculty of Mathematics and Computer Science, Ovidius University, Bd. Mamaia 124, 900527 Constanţa, Romania

²

Doctoral School of Mathematics, Ovidius University of Constanţa, 900470 Constanţa, Romania

^*

Author to whom correspondence should be addressed.

^†

These authors contributed equally to this work.

Axioms 2024, 13(6), 351; https://doi.org/10.3390/axioms13060351

Submission received: 27 March 2024 / Revised: 19 May 2024 / Accepted: 21 May 2024 / Published: 24 May 2024

(This article belongs to the Special Issue Advances in Classical and Applied Mathematics)

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Abstract

In this paper, we provide some properties of k-potent elements in algebras obtained by the Cayley–Dickson process over

Z_{p}

. Moreover, we find a structure of nonunitary ring over Fibonacci quaternions over

Z_{3}

and we present a method to encrypt plain texts, by using invertible elements in some of these algebras.

Keywords: k-potent elements; algebras obtained by the Cayley–Dickson process; quaternion Fibonacci elements

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MDPI and ACS Style

Flaut, C.; Baias, A. Some Remarks Regarding Special Elements in Algebras Obtained by the Cayley–Dickson Process over Z_p. Axioms 2024, 13, 351. https://doi.org/10.3390/axioms13060351

AMA Style

Flaut C, Baias A. Some Remarks Regarding Special Elements in Algebras Obtained by the Cayley–Dickson Process over Z_p. Axioms. 2024; 13(6):351. https://doi.org/10.3390/axioms13060351

Chicago/Turabian Style

Flaut, Cristina, and Andreea Baias. 2024. "Some Remarks Regarding Special Elements in Algebras Obtained by the Cayley–Dickson Process over Z_p" Axioms 13, no. 6: 351. https://doi.org/10.3390/axioms13060351

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Some Remarks Regarding Special Elements in Algebras Obtained by the Cayley–Dickson Process over Z_p

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