Perfect Pairs of Ideals and Duals in Numerical Semigroups

2005/08/31 by Kurt Herzinger, Herzinger, Kurt, Stephen Wilson +6
Mathematics · #20M14 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Graph theory and applications #Rings, Modules, and Algebras #math.AC #math.AG #msc:20M14

paper · pdf · doi:10.48550/arxiv.math/0508631

arxiv created 2005/08/31 · openalex publication_date 2005/08/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper considers numerical semigroups S that have a non-principal relative ideal I such that μ_S(I)μ_S(S-I)=μ_S(I+(S-I)) . We show the existence of an infinite family of such which I+(S-I)=S\backslash\0\. We also show examples of such pairs that are not members of this family. We discuss the computational process used to find these examples and present some open questions pertaining to them.

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