The Ideal Intersection Property for Groupoid Graded Rings
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The Ideal Intersection Property for Groupoid Graded Rings. / Öinert, Per Johan; Lundström, Patrik.
I: Communications in Algebra, Bind 40, Nr. 5, 2012, s. 1860-1871.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - The Ideal Intersection Property for Groupoid Graded Rings
AU - Öinert, Per Johan
AU - Lundström, Patrik
PY - 2012
Y1 - 2012
N2 - 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.
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.
U2 - 10.1080/00927872.2011.559181
DO - 10.1080/00927872.2011.559181
M3 - Journal article
VL - 40
SP - 1860
EP - 1871
JO - Communications in Algebra
JF - Communications in Algebra
SN - 0092-7872
IS - 5
ER -
ID: 49697530