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.
Similar content being viewed by others
References
Clark, J., Holton, D.A.: A First Look at Graph Theory. World Scientific, Singapore (1991)
Elduque, A., Labra, A.: Evolution algebras and graphs. J. Algebra Appl. 14(7), 1550103 (2015). 10 pp
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)
Tian, J.P.: Evolution Algebras and their Applications. Lecture Notes in Mathematics, vol. 1921. Springer, Berlin (2008)
Tian, J.P., Vojtechovsky, P.: Mathematical concepts of evolution algebras in non-mendelian genetics. Quasigroups Relat. Syst. 14(1), 111–122 (2006)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
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
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12190-020-01493-7