RT Journal Article
T1 On the subalgebra lattice of solvable evolution algebras
A1 Ladra González, Manuel
A1 Páez Guillán, María Pilar
A1 Pérez Rodríguez, Andrés
K1 Evolution algebras
K1 Solvable evolution algebras
K1 Subalgebra lattice
K1 Distributive lattice
K1 Modular lattice
K1 Semimodular lattice
AB 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.
PB Springer
SN 1578-7303
YR 2025
FD 2025-06-26
LK https://hdl.handle.net/10347/42654
UL https://hdl.handle.net/10347/42654
LA eng
NO 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
NO 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).
DS Minerva
RD 28 abr 2026