Ideal with prime radical: Difference between revisions
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===Symbol-free definition=== | ===Symbol-free definition=== | ||
An [[ideal]] in a [[commutative unital ring]] is said to have '''prime | An [[ideal]] in a [[commutative unital ring]] is said to have '''prime radical''' if its [[radical of an ideal|radical]] is a [[prime ideal]]. | ||
==Relation with other properties== | ==Relation with other properties== | ||
Revision as of 17:49, 17 December 2007
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: {{proofofstrictimplicationat|[[primary implies prime radical|prime radical not implies primary}}
- Power of a prime ideal
- Ideal with maximal radical