Ring theoretic properties of partial skew groupoid rings with applications to Leavitt path algebras

Abstract

Let [Formula: see text] be a group-type partial action of a connected groupoid [Formula: see text] on a ring [Formula: see text] and [Formula: see text] be the corresponding partial skew groupoid ring. In the first part of this paper, we investigate the relation of several ring theoretic properties between [Formula: see text] and [Formula: see text]. For the second part, using that every Leavitt path algebra is isomorphic to a partial skew groupoid ring obtained from a partial groupoid action [Formula: see text], we characterize when [Formula: see text] is group-type. In such a case, we obtain ring theoretic properties of Leavitt path algebras from the results on general partial skew groupoid rings. Several examples that illustrate the results on Leavitt path algebras are presented.