The Ideal Intersection Property for Groupoid Graded Rings

Abstract

We show that if a groupoid graded ring has a certain nonzero ideal 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.

References in corpus (1)

• Galois theory for weak Hopf algebras

Cited by in corpus (9)

• Skew Category Algebras Associated with Partially Defined Dynamical Systems
• Maximal commutative subrings and simplicity of Ore extensions
• Simplicity of skew group rings of abelian groups
• Simple Rings and Degree Maps
• Simplicity of algebras via epsilon-strong systems
• Prime group graded rings with applications to partial crossed products and Leavitt path algebras
• Simplicity of partial skew group rings and maximal commutativity
• Maximal commutative subrings and simplicity of partial skew group rings
• Graded monomial identities and almost non-degenerate gradings on matrices