Galois corings applied to partial Galois theory

TL;DR

This paper extends the concept of partial Galois extensions to noncommutative rings using Galois corings, establishing a Morita context for partial actions.

Contribution

It introduces a novel framework for partial Galois extensions in noncommutative rings via Galois corings, expanding the scope of partial Galois theory.

Findings

Established a Morita context for partial actions on rings

Extended partial Galois theory to noncommutative rings

Linked Galois corings with partial Galois extensions

Abstract

Partial Galois extensions were recently introduced by Dokuchaev, Ferrero and Paques. We introduce partial Galois extensions for noncommutative rings, using the theory of Galois corings. We associate a Morita context to a partial action on a ring.