Ideal with prime radical: Difference between revisions
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* [[Prime ideal]] | * [[Prime ideal]] | ||
* [[Primary ideal]]: {{proofofstrictimplicationat|[[primary implies prime radical|[[prime radical not implies primary]]}} | * [[Primary ideal]]: {{proofofstrictimplicationat|[[primary implies prime radical]]|[[prime radical not implies primary]]}} | ||
* [[Power of a prime ideal]] | * [[Power of a prime ideal]] | ||
* [[Ideal with maximal radical]] | * [[Ideal with maximal radical]] | ||
Revision as of 23:20, 5 January 2008
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