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Numerical Semigroups with a Fixed Fundamental Gap

Author

Listed:
  • María Ángeles Moreno-Frías

    (Department of Mathematics, Faculty of Sciences, University of Cádiz, E-11510 Puerto Real, Spain
    These authors contributed equally to this work.)

  • José Carlos Rosales

    (Department of Algebra, Faculty of Sciences, University of Granada, E-18071 Granada, Spain
    These authors contributed equally to this work.)

Abstract

A gap a of a numerical semigroup S is fundamental if { 2 a , 3 a } ⊆ S . In this work, we will study the set B ( a ) = S ∣ S is a numerical semigroup and a is a fundamental gap of S . In particular, we will give an algorithm to compute all the elements of B ( a ) with a given genus. The intersection of two elements of B ( a ) is again one element of B ( a ) . A B ( a ) -irreducible numerical semigroup is an element of B ( a ) that cannot be expressed as an intersection of two elements of B ( a ) containing it properly. In this paper, we will study the B ( a ) -irreducible numerical semigroups. In this sense we will give an algorithm to calculate all of them. Finally, we will study the submonoids of ( N , + ) that can be expressed as an intersection (finite or infinite) of elements belonging to B ( a ) .

Suggested Citation

  • María Ángeles Moreno-Frías & José Carlos Rosales, 2024. "Numerical Semigroups with a Fixed Fundamental Gap," Mathematics, MDPI, vol. 13(1), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:13:y:2024:i:1:p:95-:d:1555859
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