Prime groupoid graded rings with applications to partial skew groupoid rings

2022/11/28 by Moreira, Paula S. E., Öinert, Johan · 2 citations
#16N60 #16S35 #16S99 #16W50 #18B40 #FOS: Mathematics #Operator Algebras (math.OA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2211.15753

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.

Cited by

• Groupoid graded rings and their categories of graded modules
• Graded chain conditions and graded Jacobson radical of groupoid graded modules

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