Miyashita Action in Strongly Groupoid Graded Rings
(2012) In International Electronic Journal of Algebra 11. p.46-63- Abstract
- We determine the commutant of homogeneous subrings in strongly
groupoid graded rings in terms of an action on the ring induced by the grading. Thereby we generalize a classical result of Miyashita from the group graded case to the groupoid graded situation. In the end of the article we exemplify this result. To this end, we show, by an explicit construction, that given a finite groupoid G, equipped with a nonidentity morphism t : d(t) \to c(t), there is a strongly G-graded ring R with the properties that each R_s, for s \in G, is nonzero and R_t is a nonfree left R_{c(t)}-module.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/3409302
- author
- Öinert, Johan LU and Lundström, Patrik
- organization
- publishing date
- 2012
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- graded rings, commutants, groupoid actions, matrix algebras
- in
- International Electronic Journal of Algebra
- volume
- 11
- pages
- 46 - 63
- publisher
- Istanbul : Abdullah Hamanci
- ISSN
- 1306-6048
- language
- English
- LU publication?
- no
- id
- ab00e0c1-82cb-4d80-a46f-47e133167977 (old id 3409302)
- alternative location
- http://www.ieja.net/files/papers/volume-11/Volume-10--2011/5-V11-2012.pdf
- date added to LUP
- 2016-04-01 14:17:23
- date last changed
- 2020-05-14 15:33:35
@article{ab00e0c1-82cb-4d80-a46f-47e133167977, abstract = {{We determine the commutant of homogeneous subrings in strongly<br/><br> groupoid graded rings in terms of an action on the ring induced by the grading. Thereby we generalize a classical result of Miyashita from the group graded case to the groupoid graded situation. In the end of the article we exemplify this result. To this end, we show, by an explicit construction, that given a finite groupoid G, equipped with a nonidentity morphism t : d(t) \to c(t), there is a strongly G-graded ring R with the properties that each R_s, for s \in G, is nonzero and R_t is a nonfree left R_{c(t)}-module.}}, author = {{Öinert, Johan and Lundström, Patrik}}, issn = {{1306-6048}}, keywords = {{graded rings; commutants; groupoid actions; matrix algebras}}, language = {{eng}}, pages = {{46--63}}, publisher = {{Istanbul : Abdullah Hamanci}}, series = {{International Electronic Journal of Algebra}}, title = {{Miyashita Action in Strongly Groupoid Graded Rings}}, url = {{http://www.ieja.net/files/papers/volume-11/Volume-10--2011/5-V11-2012.pdf}}, volume = {{11}}, year = {{2012}}, }