Prime groupoid graded rings with applications to partial skew groupoid rings

TL;DR

This paper characterizes the conditions under which groupoid graded rings are prime, extending classical and recent results, with applications to partial skew groupoid rings and groupoid rings.

Contribution

It provides necessary and sufficient conditions for primeness of nearly-epsilon strongly groupoid graded rings and applies these to characterize prime partial skew groupoid rings.

Findings

Characterization of prime groupoid graded rings.

Necessary and sufficient conditions for primeness.

Extension of classical and recent results.

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.