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

Let alpha = (A(g), alpha(g))(g is an element of G) be a group-type partial action of a connected groupoid G on a ring A = circle plus(z is an element of G0) A(z) and B := A *(alpha) G be the corresponding partial skew groupoid ring. In the first part of this paper, we investigate the relation of several ring theoretic properties between A and B. For the second part, using that every Leavitt path algebra is isomorphic to a partial skew groupoid ring obtained from a partial groupoid action lambda, we characterize when lambda 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.