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Published in:
08-01-2021 | Original Research
The concept of hierarchy of algebras and graphs
Published in: Journal of Applied Mathematics and Computing | Issue 1-2/2021
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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.