Principal prime ideal

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)

Relation with other properties

Weaker properties

• Principal ideal
• Prime ideal