**Krassimir T. Atanassov**

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 29, 2023, Number 4, Pages 861–880

DOI: 10.7546/nntdm.2023.29.4.861-880

**Full paper (PDF, 267 Kb)**

## Details

### Authors and affiliations

Krassimir T. Atanassov

*Dept. of Bioinformatics and Mathematical Modelling,
Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences
105 Acad. G. Bonchev Str., 1113 Sofia, Bulgaria*

*Intelligent Systems Laboratory*

Prof. Asen Zlatarov University, Bourgas-8000, Bulgaria

Prof. Asen Zlatarov University, Bourgas-8000, Bulgaria

### Abstract

The concept of the object called “tertion” is discussed. Some operations over tertions are introduced and their properties are studied. The relationship between tertions, complex numbers are quaternions are discussed.

### Keywords

- Complex number
- Quaternion
- Tertion

### 2020 Mathematics Subject Classification

- 20G20
- 97F50

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### Manuscript history

- Received: 19 October 2023
- Revised: 17 November 2023
- Accepted: 6 December 2023
- Online First: 29 December 2023

### Copyright information

Ⓒ 2023 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).

## Related papers

- Mohammed, A. (2007). A note on rhotrix exponent rule and its applications to some special series and polynomial equations defined over rhotrices.
*Notes on Theory and Discrete Mathematics*, 13(1), 1–15. - Aminu, A. (2009). On the linear systems over rhotrices.
*Notes on Number Theory and Discrete Mathematics*, 15(4), 7–12. - Mohammed, A., & Sani, B. (2011). On construction of rhomtrees as graphical representation of rhotrices.
*Notes on Theory and Discrete Mathematics*, 17(1), 21–29. - Peter, C. M. (2012). Row-wise representation of arbitrary rhotrix.
*Notes on Number Theory and Discrete Mathematics*, 18(2), 1–27. - Mohammed, A., & Okon, U. (2016). On subgroups of non-commutative general rhotrix group.
*Notes on Number Theory and Discrete Mathematics*, 22(2), 72–90. - Isere, A. O. (2018). Even dimensional rhotrix.
*Notes on Number Theory and Discrete Mathematics*, 24(2), 125–133. - Isere, A. O. (2019). Representation of higher even-dimensional rhotrix.
*Notes on Number Theory and Discrete Mathematics*, 25(1), 206–219. - Patil, K. (2021). Characterization of ideals of rhotrices over a ring and its applications.
*Notes on Number Theory and Discrete Mathematics*, 27(1), 138–147. - Ndubuisi, R. U., Nwajeri, U. K., Onyenegecha, C. P.,Patil, K. M., Udoaka, O. G., & Osuji, W. I. (2022). Linear mappings in paraletrix spaces and their application to fractional calculus.
*Notes on Number Theory and Discrete Mathematics*, 28(4), 698–709. - Atanassov, K. (2024). On tertions and dual numbers.
*Notes on Number Theory and Discrete Mathematics*, 30(2), 443-452, DOI: 10.7546/nntdm.2024.30.2.443-452.

## Cite this paper

Atanassov, K. T. (2023). On tertions and other algebraic objects. *Notes on Number Theory and Discrete Mathematics*, 29(4), 861-880, DOI: 10.7546/nntdm.2023.29.4.861-880.