Ladra González, ManuelPérez Rodríguez, Andrés2026-05-072026-05-072025-11-16Ladra, M., Pérez-Rodríguez, A. A Frattini theory for evolution algebras. Ricerche mat 75, 701–723 (2026). https://doi.org/10.1007/s11587-025-01027-yhttps://hdl.handle.net/10347/47161This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s11587-025-01027-yThis paper develops a Frattini theory for evolution algebras defining the Frattini subalgebra as the intersection of all maximal subalgebras, and the Frattini ideal as the largest ideal contained in it. To this end, we revisit the notion of nilradical, whose classical definition is not directly applicable in this setting, and propose the supersolvable nilradical as a suitable alternative. This leads to necessary and sufficient conditions for the triviality of the Frattini subalgebra and ideal. Finally, we also briefly examine the relevance of the Frattini ideal in the study of dually atomistic evolution algebras.engEvolution algebrasFrattini subalgebraFrattini idealNilradicalDually atomisticjournal article1827-3491open access