# Definite orders with locally free cancellation

## TL;DR

This paper classifies all orders in definite quaternion algebras over number fields that possess the Hermite property, including those with the cancellation property for locally free modules, providing a comprehensive enumeration.

## Contribution

It provides the first complete enumeration of orders with the Hermite property in definite quaternion algebras over number fields, highlighting those with locally free cancellation.

## Key findings

- All orders with the Hermite property are classified.
- Includes orders with the cancellation property for locally free modules.
- Provides a comprehensive list of such orders.

## Abstract

We enumerate all orders in definite quaternion algebras over number fields with the Hermite property; this includes all orders with the cancellation property for locally free modules.