Arf good semigroups

TL;DR

This paper investigates Arf good subsemigroups of ^n, providing methods to compute all such semigroups with specified multiplicity branches and extending the concept of characters to these structures.

Contribution

It introduces a systematic way to compute Arf semigroups with given multiplicity branches and extends the concept of characters from numerical to Arf good semigroups.

Findings

Method to compute all Arf semigroups with given multiplicity branches

Extension of characters concept to Arf good semigroups

Procedure for determining Arf closure of sets and semigroups

Abstract

In this paper we study the property of the Arf good subsemigroups of $\mathbb{N}^n$, with $n\geq2$. We give a way to compute all the Arf semigroups with a given collection of multiplicity branches. We also deal with the problem of determining the Arf closure of a set of vectors and of a good semigroup, extending the concept of characters of an Arf numerical semigroup to Arf good semigroups.