Intersection of maximal ideals
This article defines a property of an ideal in a commutative unital ring |View other properties of ideals in commutative unital rings
This property of an ideal in a ring is equivalent to the property of the quotient ring being a/an: semisimple ring | View other quotient-determined properties of ideals in commutative unital rings
Definition
Symbol-free definition
An ideal in a commutative unital ring is termed an intersection of maximal ideals if it can be expressed as an intersection of maximal ideals (this is really a tautological definition).
Relation with other properties
Stronger properties
Weaker properties
- Radical ideal: For full proof, refer: Intersection of maximal ideals implies radical
Related ring properties
A ring in which every radical ideal is an intersection of maximal ideals is termed a Jacobson ring (or sometimes a Hilbert ring).