Galois Theory for Inverse Semigroup Orthogonal Actions

TL;DR

This paper establishes a Galois correspondence for inverse semigroup actions on rings, extending classical results from groupoid actions and utilizing inverse semigroup theory.

Contribution

It introduces a Galois correspondence theorem for inverse semigroup actions on rings, linking inverse semigroups and inductive groupoids.

Findings

Galois correspondence for inverse semigroup actions proved

Connection between inverse semigroups and inductive groupoids established

Extension of classical Galois theory to inverse semigroups

Abstract

A Galois correspondence theorem is proved for the case of inverse semigroups acting orthogonally on commutative rings as a consequence of the Galois correspondence theorem for groupoid actions. To this end, we use a classic result of inverse semigroup theory that establishes a one-to-one correspondence between inverse semigroups and inductive groupoids.