**Krassimir T. Atanassov**

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 30, 2024, Number 3, Pages 590–594

DOI: 10.7546/nntdm.2024.30.3.590-594

Full paper (PDF, 175 Kb)

## Details

### Authors and affiliations

Krassimir T. Atanassov

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

### Abstract

The set of ‘s for natural numbers is constructed. For this set it is proved that it is a commutative semi-group. The conditions for which it is a monoid are given.

### Keywords

- Monoid
- Natural number

### 2020 Mathematics Subject Classification

- 11A25

### References

- Atanassov, K. (2020). Objects generated by an arbitrary natural number.
*Notes on Number Theory and Discrete Mathematics*, 26(4), 57–62. - Atanassov, K. (2022). Objects generated by an arbitrary natural number. Part 2: Modal aspect.
*Notes on Number Theory and Discrete Mathematics*, 28(3), 558–563. - Atanassov, K. (2023). Objects generated by an arbitrary natural number. Part 3: Standard modal-topological aspect.
*Notes on Number Theory and Discrete Mathematics*, 29(1), 171–180. - Atanassov, K. (2023). Objects generated by an arbitrary natural number. Part 4: New aspects.
*Notes on Number Theory and Discrete Mathematics*, 29(3), 589–597. - Sandor, J., & Crstici, B. (2005).
*Handbook of Number Theory. II*. Springer Verlag, Berlin

### Manuscript history

- Received: 10 June 2024
- Revised: 29 September 2024
- Accepted: 16 October 2024
- Online First: 22 October 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).

## Related papers

- Atanassov, K. (2020). Objects generated by an arbitrary natural number.
*Notes on Number Theory and Discrete Mathematics*, 26(4), 57–62. - Atanassov, K. (2022). Objects generated by an arbitrary natural number. Part 2: Modal aspect.
*Notes on Number Theory and Discrete Mathematics*, 28(3), 558–563. - Atanassov, K. (2023). Objects generated by an arbitrary natural number. Part 3: Standard modal-topological aspect.
*Notes on Number Theory and Discrete Mathematics*, 29(1), 171–180. - Atanassov, K. (2023). Objects generated by an arbitrary natural number. Part 4: New aspects.
*Notes on Number Theory and Discrete Mathematics*, 29(3), 589–597. - Atanassov, K., & Sándor, J. (2023). On a modification of
__Set__(*n*).*Notes on Number Theory and Discrete Mathematics*, 29(4), 813-819.

## Cite this paper

Atanassov, K. T. (2024). On the set of __Set__(*n*)’s. *Notes on Number Theory and Discrete Mathematics*, 30(3), 590-594, DOI: 10.7546/nntdm.2024.30.3.590-594