A semigroup-theoretic linkage theory for relative ideals: principal and canonical links

TL;DR

This paper introduces a semigroup-theoretic framework for linking relative ideals in numerical semigroups, proposing two parallel linkage notions based on translations of the semigroup and its canonical ideal.

Contribution

It develops a novel semigroup-theoretic analogue of liaison theory for relative ideals, expanding the algebraic tools available for numerical semigroup analysis.

Findings

Proposes two linkage notions: one based on translates of the semigroup.

Establishes a theoretical foundation for semigroup liaison analogous to classical liaison theory.

Provides a new perspective on the structure of relative ideals in numerical semigroups.

Abstract

We develop a semigroup-theoretic analogue of liaison for relative ideals of a numerical semigroup. Two parallel linkage notions are proposed: a theory based on translates of the semigroup and a theory based on translates of the canonical ideal.