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.