García-Martínez, XabierPérez Rodríguez, Andrés2026-05-072026-05-072026-04-22García-Martínez, X., & Pérez-Rodríguez, A. (2026) A note on complete evolution algebras, Archiv der Mathematik. https://doi.org/10.1007/s00013-026-02251-0https://hdl.handle.net/10347/47156This 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.engThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons. org/licenses/by/4.0/.Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/Evolution algebrasComplete evolution algebrasSubalgebrasIdempotentsjournal article10.1007/s00013-026-02251-01420-8938open access