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On Ideals of Submonoids of Power Monoids

Author

Listed:
  • Juan Ignacio García-García

    (Departamento de Matemáticas/INDESS (Instituto Universitario para el Desarrollo Social Sostenible), Universidad de Cádiz, E-11510 Puerto Real, Cádiz, Spain)

  • Daniel Marín-Aragón

    (Departamento de Matemáticas, Universidad de Cádiz, E-11510 Puerto Real, Cádiz, Spain)

  • Alberto Vigneron-Tenorio

    (Departamento de Matemáticas/INDESS (Instituto Universitario para el Desarrollo Social Sostenible), Universidad de Cádiz, E-11406 Jerez de la Frontera, Cádiz, Spain)

Abstract

Let S be a numerical monoid, while a P fin ( S ) -monoid S is a monoid generated by a finite number of finite non-empty subsets of S . That is, S is a non-cancellative commutative monoid obtained from the sumset of finite non-negative integer sets. This work provides an algorithm for computing the ideals associated with some P fin ( S ) -monoids. These are the key to studying some factorization properties of P fin ( S ) -monoids and some additive properties of sumsets. This approach links computational commutative algebra with additive number theory.

Suggested Citation

  • Juan Ignacio García-García & Daniel Marín-Aragón & Alberto Vigneron-Tenorio, 2025. "On Ideals of Submonoids of Power Monoids," Mathematics, MDPI, vol. 13(4), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:4:p:584-:d:1587931
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