Outer Partial Actions and Partial Skew Group Rings

摘要

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.