%0 Journal Article 
%A Moreno Frías, María Ángeles
%A Rosales, José Carlos
%T The ideals of a numerical semigroup with embedding dimension two
%D 2023
%@ 1582-5329
%U http://hdl.handle.net/10498/35415
%X Let S and Δ be numerical semigroups. We will say that S is an
ideal of Δ if there exits X ⊆ Δ such that S = (X + Δ) ∪ {0}. In this work, we will
study the ideals of a numerical semigroup of the form ⟨a, b⟩ with a and b positive
integers such that gcd{a, b} = 1. The main results that we have obtained are the
following:
1. Given a numerical semigroup S and {a, b} ⊆ N such that gcd{a, b} = 1, we
present an algorithm that allows us to determine if S is an ideal of ⟨a, b⟩.
2. If S is a numerical semigroup, we show an algorithmic procedure to compute
the set {{a, b} ⊆ N | gcd{a, b} = 1 and S is an ideal of ⟨a, b⟩} .
3. We obtain formulas to compute the multiplicity, Frobenius number and genus
of the numerical semigroups of the form (X + ⟨a, b⟩) ∪ {0} in terms of X, a
and b.
%K Numerical semigroup
%K ideal
%K I(S)-semigroup
%K embeding dimension
%K ideal dimension
%K Frobenius number
%K genus
%K multiplicity
%~ Universidad de Cádiz