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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

Published online by Cambridge University Press:  18 July 2019

DANIEL GONÇALVES Open the ORCID record for DANIEL GONÇALVES [Opens in a new window]  and
DANILO ROYER Open the ORCID record for DANILO ROYER [Opens in a new window]
DANIEL GONÇALVES*
Affiliation:
Department of Mathematics, Federal University of Santa Catarina, 88040900, Brazil
DANILO ROYER
Affiliation:
Department of Mathematics, Federal University of Santa Catarina, 88040900, Brazil email: daniloroyer@gmail.com
*
email: daemig@gmail.com
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Abstract

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.

Keywords

ultragraph Leavitt path algebraspartial skew group ringsimplicityartinian ringnoetherian ring

MSC classification

Primary: 16S35: Twisted and skew group rings, crossed products
Secondary: 16S99: None of the above, but in this section 16P20: Artinian rings and modules
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 109 , Issue 3 , December 2020 , pp. 299 - 319
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Copyright
© 2019 Australian Mathematical Publishing Association Inc.

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Footnotes

Communicated by A. Sims

Partially supported by CNPq and Capes-PrInt Brazil.

References

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