Miyashita Action in Strongly Groupoid Graded Rings
Författare
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.
Publiceringsår
2012
Språk
Engelska
Sidor
46-63
Publikation/Tidskrift/Serie
International Electronic Journal of Algebra
Volym
11
Länkar
Dokumenttyp
Artikel i tidskrift
Förlag
Istanbul : Abdullah Hamanci
Ämne
- Mathematics
Nyckelord
- graded rings
- commutants
- groupoid actions
- matrix algebras
Status
Published
Forskningsgrupp
- Non-commutative Geometry
ISBN/ISSN/Övrigt
- ISSN: 1306-6048