Galois Correspondence for Partial Groupoid Actions

TL;DR

This paper establishes a Galois correspondence framework for partial and global actions of groupoids on commutative rings, expanding understanding of symmetries in algebraic structures.

Contribution

It introduces a Galois correspondence for orthogonal partial groupoid actions and extends it to non-orthogonal cases, including strongly Galois and global actions.

Findings

Galois correspondence for orthogonal partial groupoid actions

Extension to non-orthogonal partial actions

Examples illustrating the theoretical results

Abstract

We prove a Galois correspondence theorem for groupoids acting orthogonally and partially on commutative rings. We also consider partial actions that are not orthogonal, presenting two correspondences in this case: one for strongly Galois partial groupoid actions and one for global groupoid actions (without restriction). Some examples are presented.