# Embedding dimension of a good semigroup

## TL;DR

This paper investigates the embedding dimension of good semigroups in , focusing on their properties and similarities to numerical semigroups, especially in the case of =2.

## Contribution

It introduces the concept of embedding dimension for good semigroups and explores its properties, linking it to known concepts in numerical semigroup theory.

## Key findings

- Embedding dimension defined for good semigroups.
- Properties of embedding dimension in =2 align with numerical semigroup concepts.
- Provides foundational understanding for algebraic applications.

## Abstract

In this paper, we study good semigroups of \mathbb{N}^n, a class of semigroups that contains the value semigroups of algebroid curves with n branches. We give the definition of embedding dimension of a good semigroup showing that, in the case of good semigroups of \mathbb{N}^2, some of its properties agree with the analogue concepts defined for numerical semigroups.