Prime groupoid graded rings with applications to partial skew groupoid rings

Abstract

In this paper, we investigate primeness of groupoid graded rings. We provide a set of necessary and sufficient conditions for primeness of a nearly-epsilon strongly groupoid graded ring. Furthermore, we apply our main result to get a characterization of prime partial skew groupoid rings, and in particular of prime groupoid rings, thereby generalizing a classical result by Connell and partially generalizing recent results by Steinberg.

KEYWORDS:

• Group-type partial action
• groupoid graded ring
• nearly epsilon-strongly groupoid graded ring
• partial skew groupoid ring
• prime ring

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 16W50
• 16N60
• 16S35
• 16S99
• 16W10

Acknowledgments

The authors are grateful to Patrik Lundström for making them aware of Munn’s result in [14].

Disclosure statement

The authors report that there are no competing interests to declare.

Additional information

Funding

The first named author was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES)