The lattice of ideals of a numerical semigroup and its Frobenius restricted variety associated
Maria Angeles Moreno-Frías, José Carlos Rosales
Received March 8, 2023. Published online October 23, 2023.
Abstract: Let $\Delta$ be a numerical semigroup. In this work we show that $\mathcal{J}(\Delta) =\{I\cup\nobreak\{0\} I is an ideal of \Delta\}$ is a distributive lattice, which in addition is a Frobenius restricted variety. We give an algorithm which allows us to compute the set $\mathcal{J}_a(\Delta)=\{S\in\mathcal{J}(\Delta) \max(\Delta\backslash S)=a\}$ for a given $a\in\Delta.$ As a consequence, we obtain another algorithm that computes all the elements of $\mathcal{J}(\Delta)$ with a fixed genus.
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Affiliations: Maria Angeles Moreno-Frías (corresponding author), Dpto. de Matemáticas, Facultad de Ciencias, Universidad de Cádiz, E-11510, Puerto Real, Cádiz, Spain, e-mail: mariangeles.moreno@uca.es; José Carlos Rosales, Dpto. de Álgebra, Facultad de Ciencias, Universidad de Granada, E-18071, Granada, Spain, e-mail: jrosales@ugr.es
