RT journal article
T1 The ideals of a numerical semigroup with embedding dimension two
A1 Moreno Frías, María Ángeles
A1 Rosales, José Carlos
A2 Matemáticas
K1 Numerical semigroup
K1 ideal
K1 I(S)-semigroup
K1 embeding dimension
K1 ideal dimension
K1 Frobenius number
K1 genus
K1 multiplicity
AB Let S and Δ be numerical semigroups. We will say that S is anideal of Δ if there exits X ⊆ Δ such that S = (X + Δ) ∪ {0}. In this work, we willstudy the ideals of a numerical semigroup of the form ⟨a, b⟩ with a and b positiveintegers such that gcd{a, b} = 1. The main results that we have obtained are thefollowing:1. Given a numerical semigroup S and {a, b} ⊆ N such that gcd{a, b} = 1, wepresent 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 computethe 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 genusof the numerical semigroups of the form (X + ⟨a, b⟩) ∪ {0} in terms of X, aand b.
SN 1582-5329
YR 2023
FD 2023
LK http://hdl.handle.net/10498/35415
UL http://hdl.handle.net/10498/35415
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026