Basic ideals in evolution algebras

被引：13

作者：

Cabrera Casado, Yolanda ^{[1
]}

Kanuni, Muge ^{[2
]}

Siles Molina, Mercedes ^{[1
]}

机构：

[1] Univ Malaga, Dept Matemat Aplicada, Campus Teatinos S-N, E-29071 Malaga, Spain

[2] Duzce Univ, Dept Math, TR-81620 Konuralp, Duzce, Turkey

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2019年 / 570卷

关键词：

Genetic algebra; Evolution algebra; Simple algebra; Perfect algebra; Basic ideal; Irreducible algebra;

D O I：

10.1016/j.laa.2019.01.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：148 / 180

页数：33

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