A note on complete evolution algebras

Archiv der Mathematik 2026 Open access

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Authors: Xabier García‐Martínez, Andrés Pérez-Rodríguez
DOI: 10.1007/s00013-026-02251-0
Cited by: 0
References: 12

Abstract

Abstract This short note provides positive answers to two conjectures of Camacho, Khudoyberdiyev, and Omirov on the classification of complete evolution algebras. Our approach is based on analysing the solution set of a generic non-linear polynomial system of equations using elementary tools from algebraic geometry. We also obtain new results on subalgebras and idempotents of evolution algebras, and conclude by proposing a conjecture that may characterise solvable evolution algebras.

Fields of Study & Subjects

Advanced Topics in Algebra Polynomial and algebraic computation Advanced Differential Equations and Dynamical Systems

Publication details

Journal / source
Archiv der Mathematik
Publisher
Springer Science and Business Media LLC
Volume
126
Issue
6
Pages
597–604
Publication date
22 April 2026
Language
EN