On Ideals of Submonoids of Power Monoids

Juan Ignacio García-García, Daniel Marín-Aragón and Alberto Vigneron-Tenorio ()
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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

Mathematics, 2025, vol. 13, issue 4, 1-14

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.

Keywords: atomic monoid; elasticity; h-fold sumset; non-cancellative monoid; power monoid; monoid ideal; semigroup ideal; sumset (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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