Outer Partial Actions and Partial Skew Group Rings
Printed: Oct 2015
We extend the classicial 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.
outer action, partial action, minimality, topological dynamics, partial skew group ring, simplicity
16W50 - Graded rings and modules
37B05 - Transformations and group actions with special properties (minimality, distality, proximality, etc.)
37B99 - None of the above, but in this section
54H15 - Transformation groups and semigroups [See also 20M20, 22-XX, 57Sxx]
54H20 - Topological dynamics [See also 28Dxx, 37Bxx]