Embedding Boolean ample monoids as full submonoids of Boolean inverse monoids

TL;DR

This paper demonstrates conditions under which Boolean ample monoids can be embedded into Boolean inverse monoids, extending known embedding results using advanced algebraic tools.

Contribution

It generalizes the embedding of right reversible cancellative monoids into groups to the setting of Boolean ample and inverse monoids using groupoids and duality theories.

Findings

Boolean ample monoids can be embedded into Boolean inverse monoids under certain conditions.

The embedding generalizes the classical embedding of right reversible cancellative monoids into groups.

Groupoids of fractions and non-commutative Stone duality are key tools in the proof.

Abstract

We show that, in certain circumstances, a Boolean ample monoid may be fully embedded into a Boolean inverse monoid in a way that generalizes how right reversible cancellative monoids may be embedded into groups. We use groupoids of fractions and non-commutative Stone duality to prove the result.