On the Galois map for groupoid actions

TL;DR

This paper investigates conditions under which the Galois map is injective in the context of groupoid actions on noncommutative rings, providing a full characterization for bijectivity in central Galois algebras.

Contribution

It offers new criteria for the injectivity of the Galois map and characterizes when it is bijective for central Galois algebras.

Findings

Conditions for Galois map injectivity established

Complete characterization of bijective Galois maps in central Galois algebras

Extension of Galois theory to groupoid actions on noncommutative rings

Abstract

Some conditions for the Galois map to be injective are given in the groupoid acting on a noncommutative ring context. In the particular case in which the Galois extension is a central Galois algebra, it is given a complete characterization of that kind of extension with Galois map bijective.