The isomorphism problem for ideal class monoids of numerical semigroups

2023/11/26 by Pedro A. García-Sánchez, Garcia-Sanchez, Pedro A.
Mathematics · #06A06 #06F05 #20M12 #20M13 #20M14 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2311.15265

openalex publication_date 2023/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

From any poset isomorphic to the poset of gaps of a numerical semigroup S with the order induced by S, one can recover S. As an application, we prove that two different numerical semigroups cannot have isomorphic posets (with respect to set inclusion) of ideals whose minimum is zero. We also show that given two numerical semigroups S and T, if their ideal class monoids are isomorphic, then S must be equal to T.

Related

• When the poset of the ideal class monoid of a numerical semigroup is a lattice
• The poset of normalized ideals of numerical semigroups with multiplicity three
• Apéry sets and the ideal class monoid of a numerical semigroup
• Enumerating numerical sets associated to a numerical semigroup
• Perfect Pairs of Ideals and Duals in Numerical Semigroups