Objects generated by an arbitrary natural number. Part 2: Modal aspect

Krassimir T. Atanassov
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 3, Pages 558–563
DOI: 10.7546/nntdm.2022.28.3.558-563
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Authors and affiliations

Krassimir T. Atanassov
1 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
e-mail: krat@bas.bg

2 Intelligent Systems Laboratory, “Prof. Dr. Asen Zlatarov” University
Bourgas-8010, Bulgaria

Abstract

The set Set(n), generated by an arbitrary natural number n, was defined in [2] and some arithmetic functions, defined over its elements are introduced in an algebraic aspect. Here, over the elements of Set(n), two arithmetic functions similar to the modal type of operators are defined and some of their basic properties are studied.

Keywords

  • Arithmetic functions
  • Modal operators
  • Natural numbers
  • Sets

2020 Mathematics Subject Classification

  • 11A25

References

  1. Atanassov, K. (1985). Short proof of a hypothesis of A. Mullin. Bulletin of Number Theory and Related Topics, IX(2), 9–11.
  2. Atanassov, K. (2020). Objects generated by an arbitrary natural number. Notes on Number Theory and Discrete Mathematics, 26(4), 57–62.
  3. Atanassov, K. (2022). On the intuitionistic fuzzy modal feeble topological structures. Notes on Intuitionistic Fuzzy Sets, 28(3), 211–222.
  4. Blackburn, P., van Benthem, J., & Wolter, F. (2006) Modal Logic. North Holland,
    Amsterdam.
  5. BBourbaki, N. (1960). Éléments De Mathématique, Livre III: Topologie Générale, Chapitre 1: Structures Topologiques, Chapitre 2: Structures Uniformes. Herman, Paris (Third edition, in French).
  6. Feys, R. (1965). Modal Logics. Gauthier, Paris.
  7. Fitting, M., & Mendelsohn, R. (1998). First Order Modal Logic. Kluwer, Dordrecht.
  8. Kuratowski, K. (1966). Topology, Vol. 1, New York, Acad. Press.
  9. Sándor, J., & Crstici, B. (2005). Handbook of Number Theory. II. Springer Verlag, Berlin.

Manuscript history

  • Received: 20 January 2022
  • Revised: 17 July 2022
  • Accepted: 7 September 2022
  • Online First: 19 September 2022

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Cite this paper

Atanassov, K. T. (2022). Objects generated by an arbitrary natural number. Part 2: Modal aspect. Notes on Number Theory and Discrete Mathematics, 28(3), 558-563, DOI: 10.7546/nntdm.2022.28.3.558-563.

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