Advanced

The Ideal Intersection Property for Groupoid Graded Rings

Öinert, Johan LU and Lundström, Patrik (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:
author
organization
publishing date
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
2013-03-22 20:45:20
date last changed
2017-01-01 03:17:35
@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},
  keyword      = {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},
  volume       = {40},
  year         = {2012},
}