Ideal generated by prime elements

Statement

An ideal generated by prime elements is an ideal in an integral domain with a generating set, all of whose elements are primes.

Relation with other properties

Stronger properties

• Prime ideal in a unique factorization domain. For proof of the implication, refer Unique factorization implies every prime ideal is generated by prime elements, Unique factorization and Noetherian implies every prime ideal is generated by finitely many prime elements and for proof of its strictness (i.e. the reverse implication being false) refer Ideal generated by two prime elements in a unique factorization domain may be proper and not prime