Partial groupoid actions: globalization, Morita theory and Galois theory

TL;DR

This paper introduces partial groupoid actions on rings, provides criteria for their globalization, and explores their connections to Morita theory and Galois extensions, advancing the understanding of partial symmetries in algebraic structures.

Contribution

It defines partial groupoid actions on rings, establishes conditions for their globalization, and links these concepts to Morita theory and Galois extensions, offering new algebraic insights.

Findings

Criteria for the existence of globalization of partial groupoid actions

Construction of a Morita context associated to globalizable actions

Introduction of partial Galois extensions related to Morita context strictness

Abstract

In this paper we introduce the notion of a partial action of a groupoid on a ring as well as we give a criteria for the existence of a globalization of it. We construct a Morita context associated to a globalizable partial groupoid action and we introduce the notion of a partial Galois extension, which is related to the strictness of this context.