%0 Journal Article 
%A García García, Juan Ignacio
%A Moreno Frías, María Ángeles
%A Rosales, José Carlos
%A Vigneron Tenorio, Alberto
%T The complexity of a numerical semigroup
%D 2023
%@ 1727-933X

%U http://hdl.handle.net/10498/35379
%X Let S and Δ be numerical semigroups.A numerical semigroup S
is an I(Δ)-semigroup if S \ {0} is an ideal of Δ.We denote by J (Δ) = {S |
S is an I(Δ)-semigroup}, and we say that Δ is an ideal extension of S if S ∈ J (Δ).
In this work,we present an algorithm to build all the ideal extensions of a numerical semigroup.We recursively denote by J_0(N) = N, J_1(N) = J (N) and
J_{ k+1}(N) = J (J_k(N)) forall k ∈ N. The complexity of a numerical semigroup S is
the minimum of the set {k ∈ N | S ∈ J k(N)}. In addition,we introduce an algorithm
to compute all the numerical semigroups with fixed multiplicity and complexity.
%K Complexity
%K extension
%K i-chain
%K i-pertinentmap
%K ideal
%K numerical semigroup
%~ Universidad de Cádiz