A countable series of bisimple $\mathcal{H}$-trivial finitely presented congruence-free monoids

TL;DR

This paper introduces a countable series of finitely presented monoids that are bisimple, $ ext{H}$-trivial, and congruence-free, expanding the understanding of algebraic structures with these properties.

Contribution

It constructs a new infinite series of monoids with specific algebraic properties, which was not previously known.

Findings

Countable series of monoids constructed

Monoids are bisimple and $ ext{H}$-trivial

Monoids are congruence-free

Abstract

We provide a countable series of bisimple $\mathcal{H}$-trivial finitely presented congruence-free monoids.