On tertions and dual numbers

Krassimir T. Atanassov
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 30, 2024, Number 2, Pages 443–452
DOI: 10.7546/nntdm.2024.30.2.443-452
Full paper (PDF, 211 Kb)

Details

Authors and affiliations

Krassimir T. Atanassov
Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences
Acad. G. Bonchev Str., Bl. 105, Sofia – 1113, Bulgaria

Abstract

In a previous author’s paper [1], the mathematical object called “tertion” was discussed. Some operations over tertions were introduced and their properties were studied. There, it was showed that the complex numbers and quaternions can be represented by tertions. Here, we show that the dual numbers also are representable by tertions. The concept of a “0-quaternion” is introduced and its representation by tertions is given. Ideas for future research are described.

Keywords

• Dual number
• Quaternion
• Tertion
• 0-Quaternion

2020 Mathematics Subject Classification

• 11R52

References

1. Atanassov, K. (2023). On tertions and other algebraic objects. Notes on Number Theory and Discrete Mathematics, 29(4), 861–880.
2. Atanassov, K. (2023). Tertions – Strange Algebraic Objects. WIT Academy Press, Warsaw.
3. Burnside, D. (1899). Octonions – a development of Clifford’s bi-quaternions. Nature, 59, 411–412.
4. Clifford, W. (1873). Preliminary sketch of bi-quaternions. Proceedings of the London Mathematical Society, 4, 381–395.
5. Kotelnikov, A. (1895). Screw Calculus and Some of Its Applications to Geometry and Mechanics. Annals of the Imperial University of Kazan (in Russian).
6. Qi, L., Ling, C., Yan, H. (2022). Dual quaternions and dual quaternion vectors. Communications on Applied Mathematics and Computation, 4, 1494–1508.
7. Study, E. (1901). Geometrie der Dynamen. Teubner, Leipzig.

Manuscript history

• Received: 25 January 2024
• Revised: 10 June 2024
• Accepted: 28 June 2024
• Online First: 18 July 2024

Copyright information

Ⓒ 2024 by the Author.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).