Local domain: Difference between revisions
No edit summary |
m (3 revisions) |
||
| (One intermediate revision by the same user not shown) | |||
| Line 10: | Line 10: | ||
===Stronger properties=== | ===Stronger properties=== | ||
* [[Regular local ring]] | * [[Regular local ring]]: {{proofat|[[Regular local ring implies integral domain]]}} | ||
* [[Local Noetherian domain]] | |||
* [[Field]] | * [[Field]] | ||
Latest revision as of 16:26, 12 May 2008
This article defines a property of integral domains, viz., a property that, given any integral domain, is either true or false for that.
View other properties of integral domains | 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
This article defines a property that can be evaluated for a local ring
View other properties of local rings
Definition
A local domain is a local ring which is also an integral domain.
Relation with other properties
Stronger properties
- Regular local ring: For full proof, refer: Regular local ring implies integral domain
- Local Noetherian domain
- Field