Intersection of maximal ideals

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).

Note that although a maximal ideal is assumed to be proper, an intersection of maximal ideals could be the whole ring, i.e. we allow the empty intersection.

Stronger properties

 * Weaker than::Maximal ideal

Weaker properties

 * Stronger than::Radical ideal:

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).