Partial actions and an embedding theorem for inverse semigroups

TL;DR

This paper introduces a straightforward construction using partial actions to simplify the proof of a weakened version of O'Carroll's theorem on inverse semigroup extensions.

Contribution

It provides a new, simplified approach to prove a key theorem related to inverse semigroups using partial actions.

Findings

Simplified proof of a weakened O'Carroll's theorem

New construction involving partial actions

Enhanced understanding of inverse semigroup extensions

Abstract

We give a simple construction involving partial actions which permits us to obtain an easy proof of a weakened version of L. O'Carroll's theorem on idempotent pure extensions of inverse semigroups.