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SIMPLICITY AND CHAIN CONDITIONS FOR ULTRAGRAPH LEAVITT PATH ALGEBRAS VIA PARTIAL SKEW GROUP RING THEORY
Part of
- Chain conditions, growth conditions, and other forms of finiteness
- Rings and algebras arising under various constructions
DANIEL GONÇALVES, DANILO ROYER
Journal:

Journal of the Australian Mathematical Society / Volume 109 / Issue 3 / December 2020

Published online by Cambridge University Press:

18 July 2019, pp. 299-319

Print publication:

December 2020
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We realize Leavitt ultragraph path algebras as partial skew group rings. Using this realization we characterize artinian ultragraph path algebras and give simplicity criteria for these algebras.

Outer Partial Actions and Partial Skew Group Rings
Patrik Nystedt, Johan Öinert
Journal:

Canadian Journal of Mathematics / Volume 67 / Issue 5 / 01 October 2015

Published online by Cambridge University Press:

20 November 2018, pp. 1144-1160

Print publication:

01 October 2015
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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.