CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCJM
Abstract view

Outer Partial Actions and Partial Skew Group Rings

  Published:2015-03-03
 Printed: Oct 2015
  • Patrik Nystedt,
    University West, Department of Engineering Science, SE-46186 Trollh?ttan, Sweden
  • Johan Ă–inert,
    Centre for Mathematical Sciences, P.O. Box 118, Lund University, SE-22100 Lund, Sweden
Format:   LaTeX   MathJax   PDF  

Abstract

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.
Keywords: outer action, partial action, minimality, topological dynamics, partial skew group ring, simplicity outer action, partial action, minimality, topological dynamics, partial skew group ring, simplicity
MSC Classifications: 16W50, 37B05, 37B99, 54H15, 54H20 show english descriptions Graded rings and modules
Transformations and group actions with special properties (minimality, distality, proximality, etc.)
None of the above, but in this section
Transformation groups and semigroups [See also 20M20, 22-XX, 57Sxx]
Topological dynamics [See also 28Dxx, 37Bxx]
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]
 

© Canadian Mathematical Society, 2017 : https://cms.math.ca/