On partial skew groupoids rings

Abstract

Given a partial action $\alpha$ of a connected groupoid $\mathcal{G}$ on an associative ring $A$ we investigate under what conditions the partial skew groupoid ring $A{\star }_{\alpha }\mathcal{G}$ can be realized as a partial skew group ring. In such a case applications concerning to the separability, semisimplicity and Frobenius property of the ring extension $A\subset A{\star }_{\alpha }\mathcal{G}$ as well as to the artinianity of $A{\star }_{\alpha }\mathcal{G}$ are given.

The paper is a refinement of a part of the content of arXiv:1805.00885