Partial Groupoid Actions: Globalization, Morita Theory, and Galois Theory

Abstract

In this article, 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.

Key Words:

• Partial Galois extension
• Partial groupoid action
• Partial skew groupoid ring

2010 Mathematics Subject Classification:

• Primary 20L05, 16S99
• Secondary 16W22, 18B40, 20N02

ACKNOWLEDGMENTS

The authors would like to thank the referee for his(her) helpful comments.

Notes

Communicated by I. Shestakov.