Integral domain in which every irreducible is prime

Definition
An integral domain in which every irreducible is prime is an integral domain satisfying the following equivalent condition: every defining ingredient::irreducible element in it is a defining ingredient::prime element.

Stronger properties

 * Weaker than::Euclidean domain
 * Weaker than::Principal ideal domain
 * Weaker than::Bezout domain
 * Weaker than::gcd domain
 * Weaker than::Unique factorization domain

Weaker properties

 * Integral domain in which any two irreducible factorizations are equal upto ordering and associates