The Ideal Intersection Property for Groupoid Graded Rings
(2012) In Communications in Algebra 40(5). p.1860-1871- Abstract
- We show that, if a groupoid graded ring has a grading satisfying a certain nondegeneracy property, then the commutant of the center of the principal component of the ring has the ideal intersection property, that is it intersects nontrivially every nonzero ideal of the ring. Furthermore, we show that for skew groupoid algebras with commutative principal component, the principal component is maximal commutative if and only if it has the ideal intersection property.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/3409281
- author
- Öinert, Johan LU and Lundström, Patrik
- organization
- publishing date
- 2012
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Commutants, Graded rings, Ideals, Maximal commutative subrings, Skew groupoid rings
- in
- Communications in Algebra
- volume
- 40
- issue
- 5
- pages
- 1860 - 1871
- publisher
- Taylor & Francis
- external identifiers
-
- scopus:84861471705
- ISSN
- 0092-7872
- DOI
- 10.1080/00927872.2011.559181
- language
- English
- LU publication?
- no
- id
- 33911233-a07b-4439-89ce-8347022063cc (old id 3409281)
- alternative location
- http://arxiv.org/abs/1001.0303
- date added to LUP
- 2016-04-01 10:06:58
- date last changed
- 2022-01-25 19:57:12
@article{33911233-a07b-4439-89ce-8347022063cc, abstract = {{We show that, if a groupoid graded ring has a grading satisfying a certain nondegeneracy property, then the commutant of the center of the principal component of the ring has the ideal intersection property, that is it intersects nontrivially every nonzero ideal of the ring. Furthermore, we show that for skew groupoid algebras with commutative principal component, the principal component is maximal commutative if and only if it has the ideal intersection property.}}, author = {{Öinert, Johan and Lundström, Patrik}}, issn = {{0092-7872}}, keywords = {{Commutants; Graded rings; Ideals; Maximal commutative subrings; Skew groupoid rings}}, language = {{eng}}, number = {{5}}, pages = {{1860--1871}}, publisher = {{Taylor & Francis}}, series = {{Communications in Algebra}}, title = {{The Ideal Intersection Property for Groupoid Graded Rings}}, url = {{http://dx.doi.org/10.1080/00927872.2011.559181}}, doi = {{10.1080/00927872.2011.559181}}, volume = {{40}}, year = {{2012}}, }