Normal domain: Difference between revisions
(Started the page) |
No edit summary |
||
| Line 1: | Line 1: | ||
{{integral domain property}} | |||
==Definition== | ==Definition== | ||
| Line 5: | Line 7: | ||
An [[integral domain]] is said to be '''normal''' if it is [[integrally closed subring|integrally closed]] in its [[field of fractions]]. | An [[integral domain]] is said to be '''normal''' if it is [[integrally closed subring|integrally closed]] in its [[field of fractions]]. | ||
[[ | ==Relation with other properties== | ||
[[ | |||
===Stronger properties=== | |||
* [[Unique factorization domain]] | |||
* [[Principal ideal domain]] | |||
* [Euclidean domain]] | |||
* [[Dedekind domain]] | |||
===Weaker properties=== | |||
Revision as of 00:28, 17 April 2007
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
Definition
Symbol-free definition
An integral domain is said to be normal if it is integrally closed in its field of fractions.
Relation with other properties
Stronger properties
- Unique factorization domain
- Principal ideal domain
- [Euclidean domain]]
- Dedekind domain