Noncrossed Product Matrix Subrings and Ideals of Graded Rings
(2009) In Preprints in Mathematical Sciences19990101+01:00 2009(10). Abstract
 We show that if a groupoid graded ring has a certain nonzero ideal property and the principal component of the ring is commutative, then the intersection of a nonzero twosided ideal of the ring with the commutant of the principal component of the ring is nonzero. Furthermore, we show that for a skew groupoid ring with commutative principal component, the principal component is maximal commutative if and only if it is intersected nontrivially by each nonzero ideal of the skew groupoid ring. We also determine the center of strongly groupoid graded rings in terms of an action on the ring induced by the grading. In the end of the article, we show that, given a finite groupoid G, which has a nonidentity morphism, there is a ring, strongly... (More)
 We show that if a groupoid graded ring has a certain nonzero ideal property and the principal component of the ring is commutative, then the intersection of a nonzero twosided ideal of the ring with the commutant of the principal component of the ring is nonzero. Furthermore, we show that for a skew groupoid ring with commutative principal component, the principal component is maximal commutative if and only if it is intersected nontrivially by each nonzero ideal of the skew groupoid ring. We also determine the center of strongly groupoid graded rings in terms of an action on the ring induced by the grading. In the end of the article, we show that, given a finite groupoid G, which has a nonidentity morphism, there is a ring, strongly graded by G, which is not a crossed product over G. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/1445605
 author
 Öinert, Johan ^{LU} and Lundström, Patrik
 organization
 publishing date
 2009
 type
 Contribution to journal
 publication status
 unpublished
 subject
 keywords
 ideals, matrix rings, Category graded rings, crossed products
 in
 Preprints in Mathematical Sciences19990101+01:00
 volume
 2009
 issue
 10
 pages
 14 pages
 publisher
 Lund University
 external identifiers

 other:LUTFMA51122009
 ISSN
 14039338
 project
 Noncommutative Analysis of Dynamics, Fractals and Wavelets
 Noncommutative Geometry in Mathematics and Physics
 language
 English
 LU publication?
 yes
 id
 566a78fa6f6c4f3095acc4171e935b61 (old id 1445605)
 alternative location
 http://arxiv.org/PS_cache/arxiv/pdf/0907/0907.0997v1.pdf
 http://arxiv.org/abs/0907.0997
 date added to LUP
 20090728 13:14:14
 date last changed
 20161125 14:06:58
@article{566a78fa6f6c4f3095acc4171e935b61, abstract = {We show that if a groupoid graded ring has a certain nonzero ideal property and the principal component of the ring is commutative, then the intersection of a nonzero twosided ideal of the ring with the commutant of the principal component of the ring is nonzero. Furthermore, we show that for a skew groupoid ring with commutative principal component, the principal component is maximal commutative if and only if it is intersected nontrivially by each nonzero ideal of the skew groupoid ring. We also determine the center of strongly groupoid graded rings in terms of an action on the ring induced by the grading. In the end of the article, we show that, given a finite groupoid G, which has a nonidentity morphism, there is a ring, strongly graded by G, which is not a crossed product over G.}, author = {Öinert, Johan and Lundström, Patrik}, issn = {14039338}, keyword = {ideals,matrix rings,Category graded rings,crossed products}, language = {eng}, number = {10}, pages = {14}, publisher = {Lund University}, series = {Preprints in Mathematical Sciences19990101+01:00}, title = {Noncrossed Product Matrix Subrings and Ideals of Graded Rings}, volume = {2009}, year = {2009}, }