Zero-dimensional ring: Difference between revisions
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* [[Finite ring]] | * [[Finite ring]] | ||
* [[Field]] | * [[Field]] | ||
* [[Artinian ring]] | |||
===Weaker properties=== | ===Weaker properties=== | ||
* [[ | * [[Jacobson ring]] | ||
Revision as of 01:15, 10 January 2008
Definition
Symbol-free definition
A commutative unital ring is termed zero-dimensional if it satisfies the following equivalent conditions:
- It has Krull dimension zero
- Every prime ideal in it is maximal
- Any quotient ring of it that is an integral domain is also a field