# Ordered Monoids: Languages and Relations

## TL;DR

This paper provides a finite set of axioms for the class of relational, integral ordered monoids and their language interpretations, advancing the algebraic understanding of these structures.

## Contribution

It introduces a finite axiomatization for the variety generated by relational, integral ordered monoids and their language interpretations, which was previously unknown.

## Key findings

- Finite axiomatization for relational, integral ordered monoids.
- Finite axiomatization for their language interpretation.
- Enhanced algebraic understanding of these structures.

## Abstract

We give a finite axiomatization for the variety generated by relational, integral ordered monoids. As a corollary we get a finite axiomatization for the language interpretation as well.