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Basic ideals in evolution algebras
(Elsevier Science Inc, 2019) Casado, Yolanda Cabrera; Er, Müge Kanuni; Molina, Mercedes Siles
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. (C) 2019 Elsevier Inc. All rights reserved.