Perfect pairs of ideals and duals in numerical semigroups

Kurt Herzinger, Stephen E Wilson, Nandor Sieben, Jeff Rushall

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

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
Volume34
Issue number9
DOIs
StatePublished - Sep 1 2006

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Numerical Semigroup
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Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Perfect pairs of ideals and duals in numerical semigroups. / Herzinger, Kurt; Wilson, Stephen E; Sieben, Nandor; Rushall, Jeff.

In: Communications in Algebra, Vol. 34, No. 9, 01.09.2006, p. 3475-3486.

Research output: Contribution to journalArticle

Herzinger, Kurt ; Wilson, Stephen E ; Sieben, Nandor ; Rushall, Jeff. / Perfect pairs of ideals and duals in numerical semigroups. In: Communications in Algebra. 2006 ; Vol. 34, No. 9. pp. 3475-3486.
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