Casado, Yolanda CabreraEr, Müge KanuniMolina, Mercedes Siles2020-04-302020-04-3020190024-37951873-1856https://doi.org/10.1016/j.laa.2019.01.010https://hdl.handle.net/20.500.12684/2896Molina, Mercedes Siles/0000-0002-4299-5187; Kanuni, Muge/0000-0001-7436-039X; Cabrera Casado, Yolanda/0000-0003-4299-4392WOS: 000462811200007With 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.en10.1016/j.laa.2019.01.010info:eu-repo/semantics/closedAccessGenetic algebraEvolution algebraSimple algebraPerfect algebraBasic idealIrreducible algebraArticle570148180WOS:000462811200007Q1Q2