Principal prime ideal: Difference between revisions
(New page: {{curing-ideal property}} ==Definition== An ideal in a commutative unital ring is termed a '''principal prime ideal''' if it satisfies the following equivalent conditions: * It ...) |
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Revision as of 20:20, 16 March 2008
This article defines a property of an ideal in a commutative unital ring |View other properties of ideals in commutative unital rings
Definition
An ideal in a commutative unital ring is termed a principal prime ideal if it satisfies the following equivalent conditions:
- It is a principal ideal and a prime ideal
- It is generated by a prime element (or, by zero, in the event that the ring is an integral domain)