@misc{10498/35415,
year = {2023},
url = {http://hdl.handle.net/10498/35415},
abstract = {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.},
keywords = {Numerical semigroup},
keywords = {ideal},
keywords = {I(S)-semigroup},
keywords = {embeding dimension},
keywords = {ideal dimension},
keywords = {Frobenius number},
keywords = {genus},
keywords = {multiplicity},
title = {The ideals of a numerical semigroup with embedding dimension two},
doi = {10.17114/j.aua.2023.75.04},
author = {Moreno Frías, María Ángeles and Rosales, José Carlos},
}