Domain theory and mirror properties in inverse semigroups

TL;DR

This paper explores the structure of inverse semigroups through their partial order and establishes mirror properties with their idempotent semilattice, linking algebraic and domain-theoretic concepts.

Contribution

It introduces a domain-theoretic perspective on inverse semigroups, revealing mirror properties with their idempotent semilattice, which was not previously understood.

Findings

Establishment of mirror properties between inverse semigroups and their idempotent semilattice.

Application of domain theory concepts to inverse semigroup structure.

Enhanced understanding of the partial order in inverse semigroups.

Abstract

Inverse semigroups are a class of semigroups whose structure induces a compatible partial order. This partial order is examined so as to establish mirror properties between an inverse semigroup and the semilattice of its idempotent elements, such as continuity in the sense of domain theory.