Multi-algebras as tolerance quotients of algebras

TL;DR

This paper explores how multi-algebras can be represented as tolerance quotients of algebras, providing a generalized construction that ensures all multi-algebras can be obtained this way.

Contribution

It introduces a generalized construction of tolerance quotients, demonstrating that every multi-algebra can be realized through this method.

Findings

Not all multi-algebras are tolerance quotients of algebras.

A modified construction ensures every multi-algebra arises from a tolerance quotient.

The paper provides examples and theoretical proofs for the generalized approach.

Abstract

If $A$ is an algebra and \bgt is a tolerance on $A$, then $A/\bgt$ is a multi-algebra in a natural way. We give an example to show that not every multi-algebra arises in this manner. We slightly generalize the construction of $A/\bgt$ and prove that every multi-algebra arises from this modified construction.