Principal ideal ring: Difference between revisions
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{{curing property}} | |||
==Definition== | ==Definition== | ||
===Symbol-free definition=== | ===Symbol-free definition=== | ||
A [[commutative unital ring]] | A [[commutative unital ring]] is termed a '''principal ideal ring''' if every [[ideal]] in it is [[principal ideal|principal]], that is, if every ideal is generated by a single element. | ||
===Definition with symbols=== | ===Definition with symbols=== | ||
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* [[Noetherian ring]] | * [[Noetherian ring]] | ||
==Metaproperties== | |||
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Revision as of 23:01, 7 January 2008
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
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Relation with other properties
Conjunction with other properties
- Principal ideal domain is a principal ideal ring which is also an integral domain