A Frattini theory for evolution algebras

This 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 appl...

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Detalles Bibliográficos
Autores: Ladra González, Manuel, Pérez Rodríguez, Andrés
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universidad de Santiago de Compostela (USC)
Repositorio:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
Idioma:inglés
OAI Identifier:oai:dnet:minerva_____::aeeab281e6bd21d2ef30590c2819dcd3
Acceso en línea:https://hdl.handle.net/10347/47161
Access Level:acceso abierto
Palabra clave:Evolution algebras
Frattini subalgebra
Frattini ideal
Nilradical
Dually atomistic
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spelling A Frattini theory for evolution algebrasLadra González, ManuelPérez Rodríguez, AndrésEvolution algebrasFrattini subalgebraFrattini idealNilradicalDually atomisticThis 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.Springer-Verlag ItaliaUniversidade de Santiago de Compostela. Departamento de MatemáticasUniversidade de Santiago de Compostela. Centro de Investigación e Tecnoloxía Matemática de Galicia (CITMAga)20252025-11-1620252025-11-16journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10347/47161reponame:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostelainstname:Universidad de Santiago de Compostela (USC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:dnet:minerva_____::aeeab281e6bd21d2ef30590c2819dcd32026-06-15T12:47:27Z
dc.title.none.fl_str_mv A Frattini theory for evolution algebras
title A Frattini theory for evolution algebras
spellingShingle A Frattini theory for evolution algebras
Ladra González, Manuel
Evolution algebras
Frattini subalgebra
Frattini ideal
Nilradical
Dually atomistic
title_short A Frattini theory for evolution algebras
title_full A Frattini theory for evolution algebras
title_fullStr A Frattini theory for evolution algebras
title_full_unstemmed A Frattini theory for evolution algebras
title_sort A Frattini theory for evolution algebras
dc.creator.none.fl_str_mv Ladra González, Manuel
Pérez Rodríguez, Andrés
author Ladra González, Manuel
author_facet Ladra González, Manuel
Pérez Rodríguez, Andrés
author_role author
author2 Pérez Rodríguez, Andrés
author2_role author
dc.contributor.none.fl_str_mv Universidade de Santiago de Compostela. Departamento de Matemáticas
Universidade de Santiago de Compostela. Centro de Investigación e Tecnoloxía Matemática de Galicia (CITMAga)
dc.subject.none.fl_str_mv Evolution algebras
Frattini subalgebra
Frattini ideal
Nilradical
Dually atomistic
topic Evolution algebras
Frattini subalgebra
Frattini ideal
Nilradical
Dually atomistic
description This 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.
publishDate 2025
dc.date.none.fl_str_mv 2025
2025-11-16
2025
2025-11-16
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10347/47161
url https://hdl.handle.net/10347/47161
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer-Verlag Italia
publisher.none.fl_str_mv Springer-Verlag Italia
dc.source.none.fl_str_mv reponame:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
instname:Universidad de Santiago de Compostela (USC)
instname_str Universidad de Santiago de Compostela (USC)
reponame_str Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
collection Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
repository.name.fl_str_mv
repository.mail.fl_str_mv
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