Good subsemigroups of ${\mathbb{N}}^n$

Abstract

Value semigroups of non irreducible singular algebraic curves and their fractional ideals are submonoids of ${\mathbb{Z}}^n$ that are closed under infimums, have a conductor and fulfill a special compatibility property on their elements. Monoids of ${\mathbb{N}}^n$ fulfilling these three conditions are known in the literature as good semigroups and there are examples of good semigroups that are not realizable as the value semigroup of an algebraic curve. In this paper we consider good semigroups independently from their algebraic counterpart, in a purely combinatoric setting. We define the concept of good system of generators, and we show that minimal good systems of generators are unique. Moreover, we give a constructive way to compute the canonical ideal and the Arf closure of a good subsemigroup when $n=2$.

Proof of the main theorem 13 has been replaced with a shorter and easier proof

References in corpus (2)

• numericalsgps, a GAP package for numerical semigroups
• Duality on value semigroups

Cited by in corpus (1)

• The Semiring of Values of an Algebroid Curve