Miyashita Action in Strongly Groupoid Graded Rings
Author
Summary, in English
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.
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.
Publishing year
2012
Language
English
Pages
46-63
Publication/Series
International Electronic Journal of Algebra
Volume
11
Links
Document type
Journal article
Publisher
Istanbul : Abdullah Hamanci
Topic
- Mathematics
Keywords
- graded rings
- commutants
- groupoid actions
- matrix algebras
Status
Published
Research group
- Non-commutative Geometry
ISBN/ISSN/Other
- ISSN: 1306-6048