Basic ideals in evolution algebras

With the aim of finding useful tools and invariants to classify finite dimensional evolution algebras, we introduce and study the notion of a basic ideal. Every n-dimensional perfect evolution algebra has a maximal basic ideal I which is unique except when the dimension of I is n-1. An application o...

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Bibliographic Details
Published in:Linear algebra and its applications 2019-06, Vol.570, p.148-180
Main Authors: Casado, Yolanda Cabrera, Kanuni, Müge, Siles Molina, Mercedes
Format: Article
Language:English
Subjects:
Algebra
Basic ideal
Evolution
Evolution algebra
Genetic algebra
Irreducible algebra
Linear algebra
Perfect algebra
Simple algebra
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Summary:With the aim of finding useful tools and invariants to classify finite dimensional evolution algebras, we introduce and study the notion of a basic ideal. Every n-dimensional perfect evolution algebra has a maximal basic ideal I which is unique except when the dimension of I is n-1. An application of our results leads to the description of the four dimensional perfect non-simple evolution algebras over a field with mild restrictions.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2019.01.010