Ideal with prime radical

This article defines a property of an ideal in a commutative unital ring |View other properties of ideals in commutative unital rings

Definition

Symbol-free definition

An ideal in a commutative unital ring is said to have prime radical if its radical is a prime ideal.

Relation with other properties

Stronger properties

• Prime ideal
• Primary ideal: For proof of the implication, refer primary implies prime radical and for proof of its strictness (i.e. the reverse implication being false) refer prime radical not implies primary
• Power of a prime ideal
• Ideal with maximal radical