A Frattini theory for evolution algebras

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dc.contributor.affiliationUniversidade de Santiago de Compostela. Departamento de Matemáticas
dc.contributor.affiliationUniversidade de Santiago de Compostela. Centro de Investigación e Tecnoloxía Matemática de Galicia (CITMAga)
dc.contributor.authorLadra González, Manuel
dc.contributor.authorPérez Rodríguez, Andrés
dc.date.accessioned2026-05-07T12:05:48Z
dc.date.available2026-05-07T12:05:48Z
dc.date.issued2025-11-16
dc.descriptionThis 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-y
dc.description.abstractThis 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.
dc.description.peerreviewedSI
dc.identifier.citationLadra, M., Pérez-Rodríguez, A. A Frattini theory for evolution algebras. Ricerche mat 75, 701–723 (2026). https://doi.org/10.1007/s11587-025-01027-y
dc.identifier.essn1827-3491
dc.identifier.urihttps://hdl.handle.net/10347/47161
dc.journal.titleRicerche di matematica
dc.language.isoeng
dc.publisherSpringer-Verlag Italia
dc.relation.publisherversionhttps://doi.org/10.1007/s11587-025-01027-y
dc.rights.accessRightsopen access
dc.subjectEvolution algebras
dc.subjectFrattini subalgebra
dc.subjectFrattini ideal
dc.subjectNilradical
dc.subjectDually atomistic
dc.titleA Frattini theory for evolution algebras
dc.typejournal article
dc.type.hasVersionAM
dspace.entity.typePublication
relation.isAuthorOfPublication2b7d6a14-fd3c-41da-a849-ff485bf2c3bc
relation.isAuthorOfPublication.latestForDiscovery2b7d6a14-fd3c-41da-a849-ff485bf2c3bc

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