On the subalgebra lattice of solvable evolution algebras

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URI: https://hdl.handle.net/10347/42654
ISSN: 1578-7303
E-ISSN: 1579-1505
DOI: 10.1007/s13398-025-01752-x

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2025-06-26

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Springer
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Abstract

The main objective of this paper is to study the relationship between a solvable evolution algebra and its subalgebra lattice, emphasizing two of its main properties: distributivity and modularity. First, we will focus on the nilpotent case, where distributivity is characterised, and a necessary condition for modularity is deduced. Subsequently, we comment on some results for solvable non-nilpotent evolution algebras, finding that the ones with maximum index of solvability have the best properties. Finally, we characterise modularity in this particular case by introducing supersolvable evolution algebras and computing the terms of the derived series.

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Evolution algebras| Solvable evolution algebras| Subalgebra lattice| Distributive lattice| Modular lattice| Semimodular lattice

Bibliographic citation

Ladra, M., Páez-Guillán, P. & Pérez-Rodríguez, A. On the subalgebra lattice of solvable evolution algebras. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 119, 83 (2025). https://doi.org/10.1007/s13398-025-01752-x

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Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. This work was partially supported by Agencia Estatal de Investigación (Spain), grant PID2020-115155GB-I00 (European FEDER support included, UE) and by Xunta de Galicia through the Competitive Reference Groups (GRC), ED431C 2023/31. The third author was also supported by FPU21/05685 scholarship, Ministerio de Educación y Formación Profesional (Spain).

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© The Author(s) 2025. This 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.
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