Principal ideal ring
This article defines a property of commutative unital rings; a property that can be evaluated for a commutative unital ring
View all properties of commutative unital rings
VIEW RELATED: Commutative unital ring property implications | Commutative unital ring property non-implications |Commutative unital ring metaproperty satisfactions | Commutative unital ring metaproperty dissatisfactions | Commutative unital ring property satisfactions | Commutative unital ring property dissatisfactions
Definition
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.
Definition with symbols
Fill this in later
Relation with other properties
Conjunction with other properties
- Principal ideal domain is a principal ideal ring which is also an integral domain