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 ideal if its radical is a prime ideal.
Relation with other properties
Stronger properties
- Prime ideal
- Primary ideal: {{proofofstrictimplication|[[primary implies prime radical|prime radical not implies primary}}
- Power of a prime ideal
- Ideal with maximal radical