English

Perfect Pairs of Ideals and Duals in Numerical Semigroups

Commutative Algebra 2007-05-23 v1 Algebraic Geometry

Abstract

This paper considers numerical semigroups SS that have a non-principal relative ideal II such that μS(I)μS(SI)=μS(I+(SI))\mu_S(I)\mu_S(S-I)=\mu_S(I+(S-I)) . We show the existence of an infinite family of such which I+(SI)=S\{0}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.

Keywords

Cite

@article{arxiv.math/0508631,
  title  = {Perfect Pairs of Ideals and Duals in Numerical Semigroups},
  author = {Kurt Herzinger and Stephen Wilson and Nándor Sieben and Jeff Rushall},
  journal= {arXiv preprint arXiv:math/0508631},
  year   = {2007}
}