2025/02/08 by M. Ladra, Ladra, Manuel, Pilar Páez-Guillán +3
Mathematics · #06C05 #06C10 #06D05 #17A60 #17B30 #17D92 #Advanced Topics in Algebra #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2502.05619
openalex publication_date 2025/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.