Basic Ideals in evolution algebras

Abstract

Recently a new type of genetic algebras, denominated evolution algebras, has emerged to enlighten the study of non-Mendelian genetics, which is the basic language of the molecular Biology. With the aim of finding invariants to classify finite dimensional evolution algebras, we introduce and study the notion of a basic ideal. An application of our results leads to the description of the four dimensional perfect non-simple evolution algebras over a field with mild restrictions.