The Ideal Intersection Property for Groupoid Graded Rings

Per Johan Öinert; Patrik Lundström

doi:10.1080/00927872.2011.559181

The Ideal Intersection Property for Groupoid Graded Rings

Per Johan Öinert, Patrik Lundström

Institut for Matematiske Fag

16 Citationer (Scopus)

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.

Originalsprog	Engelsk
Tidsskrift	Communications in Algebra
Vol/bind	40
Udgave nummer	5
Sider (fra-til)	1860-1871
ISSN	0092-7872
DOI	https://doi.org/10.1080/00927872.2011.559181
Status	Udgivet - maj 2012

Adgang til dokumentet

10.1080/00927872.2011.559181

Citationsformater

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AB - 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.

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