Skip to main content
SpringerLink
Log in

The concept of hierarchy of algebras and graphs

  • Original Research
  • Published:
Journal of Applied Mathematics and Computing Aims and scope Submit manuscript

Abstract

This paper deals with the concept of hierarchy of algebras and graphs. In the case of algebras, the work constitutes a generalization to any algebra of the concept of hierarchy that Tian gave for a particular type of them, evolution algebras, via concepts of occurrence and persistence. This new hierarchy proves to be invariant under isomorphism of algebras, which leads to a necessary condition for two generic algebras to be isomorphic. Furthermore, the task of how to effectively obtain the hierarchy of an algebra is also discussed, arriving to the association of a certain type of graphs to generic algebras, which leads us to introduce new concepts, based in hierarchy, in graph theory.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Clark, J., Holton, D.A.: A First Look at Graph Theory. World Scientific, Singapore (1991)

    Book  Google Scholar 

  2. Elduque, A., Labra, A.: Evolution algebras and graphs. J. Algebra Appl. 14(7), 1550103 (2015). 10 pp

    Article  MathSciNet  Google Scholar 

  3. Núñez, J., Silvero, M., Villar-Liñán, M.T.: Mathematical tools for the future: graph theory and graphicable algebras. Appl. Math. Comput. 219, 6113–6125 (2013)

    MathSciNet  MATH  Google Scholar 

  4. Tian, J.P.: Evolution Algebras and their Applications. Lecture Notes in Mathematics, vol. 1921. Springer, Berlin (2008)

    Book  Google Scholar 

  5. Tian, J.P., Vojtechovsky, P.: Mathematical concepts of evolution algebras in non-mendelian genetics. Quasigroups Relat. Syst. 14(1), 111–122 (2006)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Geometría y Topología, Universidad de Sevilla, Sevilla, Spain

    Francisco J. Cruz, Abraham Del Valle, Juan Núñez-Valdés & Manuel Pena

Authors
  1. Francisco J. Cruz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Abraham Del Valle
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Juan Núñez-Valdés
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Manuel Pena
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Juan Núñez-Valdés.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cruz, F.J., Valle, A.D., Núñez-Valdés, J. et al. The concept of hierarchy of algebras and graphs. J. Appl. Math. Comput. 67, 233–255 (2021). https://doi.org/10.1007/s12190-020-01493-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12190-020-01493-7

Keywords

Search

Navigation