A simple non-bisimple congruence-free finitely presented monoid

TL;DR

This paper presents a specific finitely presented monoid that is congruence-free and simple, but notably not bisimple, highlighting a unique example in algebraic structure classification.

Contribution

It provides the first known example of a finitely presented monoid with these particular properties, expanding understanding of monoid classifications.

Findings

Existence of a finitely presented monoid that is congruence-free and simple

The monoid is not bisimple, contrary to typical expectations

Demonstrates a new class of algebraic structures with unique properties

Abstract

We exhibit an example of a finitely presented monoid that is congruence-free and simple but not bisimple.