Published online by Cambridge University Press: 20 November 2018
We extend the classical notion of an outer action $\alpha $ of a group
$G$ on a unital ring
$A$ to the case when
$\alpha $ is a partial action on ideals, all of which have local units. We show that if
$\alpha $ is an outer partial action of an abelian group
$G$, then its associated partial skew group ring
$A\,{{\star }_{\alpha }}\,G$ is simple if and only if
$A$ is
$G$-simple. This result is applied to partial skew group rings associated with two different types of partial dynamical systems.