Perfect pairs of ideals and duals in numerical semigroups

Kurt Herzinger, Stephen Wilson, Nándor Sieben, Jeff Rushall

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


This article considers numerical semigroups S that have a nonprincipal relative ideal I such that μS(I)μS(S - I) = μS(I + (S - I)). We show the existence of an infinite family of such pairs (S, I) in which I + (S - I) = S\{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.

Original languageEnglish (US)
Pages (from-to)3475-3486
Number of pages12
JournalCommunications in Algebra
Issue number9
StatePublished - Sep 1 2006


  • Dual
  • Minimal generating set
  • Numerical semigroup
  • Relative ideal

ASJC Scopus subject areas

  • Algebra and Number Theory


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