Outer Partial Actions and Partial Skew Group Rings
(2015) In Canadian Journal of Mathematics 67(5). p.1144-1160- Abstract
- 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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/8221337
- author
- Nystedt, Patrik and Öinert, Johan LU
- organization
- publishing date
- 2015
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- outer action, partial action, minimality, topological dynamics, partial, skew group ring, simplicity
- in
- Canadian Journal of Mathematics
- volume
- 67
- issue
- 5
- pages
- 1144 - 1160
- publisher
- Canadian Mathematical Society
- external identifiers
-
- wos:000362152600008
- scopus:84976400598
- ISSN
- 0008-414X
- DOI
- 10.4153/CJM-2014-043-8
- language
- English
- LU publication?
- yes
- id
- 5e71b36f-9981-4da2-8f91-c8704d9a6d1f (old id 8221337)
- date added to LUP
- 2016-04-01 13:10:19
- date last changed
- 2022-01-27 17:45:26
@article{5e71b36f-9981-4da2-8f91-c8704d9a6d1f, abstract = {{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.}}, author = {{Nystedt, Patrik and Öinert, Johan}}, issn = {{0008-414X}}, keywords = {{outer action; partial action; minimality; topological dynamics; partial; skew group ring; simplicity}}, language = {{eng}}, number = {{5}}, pages = {{1144--1160}}, publisher = {{Canadian Mathematical Society}}, series = {{Canadian Journal of Mathematics}}, title = {{Outer Partial Actions and Partial Skew Group Rings}}, url = {{http://dx.doi.org/10.4153/CJM-2014-043-8}}, doi = {{10.4153/CJM-2014-043-8}}, volume = {{67}}, year = {{2015}}, }