# Are Ramsey Algebras Essentially Semigroups

## TL;DR

This paper investigates the importance of associativity in Ramsey algebras by examining nonassociative structures, demonstrating that the octonions' Moufang loop does not qualify as a Ramsey algebra.

## Contribution

It provides new insights into the role of associativity in Ramsey algebras by analyzing a nonassociative example, the octonions' Moufang loop.

## Key findings

- Semigroups are Ramsey algebras.
- The octonions' Moufang loop is not a Ramsey algebra.
- Associativity is crucial for a binary system to be a Ramsey algebra.

## Abstract

It is known that semigroups are Ramsey algebras. This paper is an attempt to understand the role associativity plays in a binary system being a Ramsey algebra. Specifically, we show that the nonassociative Moufang loop of octonions is not a Ramsey algebra.