Principal ideal ring

Symbol-free definition
A commutative unital ring is termed a principal ideal ring if every ideal in it is principal, that is, if every ideal is generated by a single element.

Conjunction with other properties

 * Weaker than::Principal ideal domain is a principal ideal ring which is also an integral domain

Weaker properties

 * Stronger than::Bezout ring
 * Stronger than::Noetherian ring
 * Stronger than::One-dimensional ring: