isDedekindDomain
P27196
predicate
Indicates that a ring is a Dedekind domain, meaning it is a Noetherian, integrally closed integral domain of Krull dimension one in which every nonzero ideal factors uniquely into prime ideals.
All labels observed (2)
| Label | Occurrences |
|---|---|
| hasUniqueFactorizationOfIdeals | 1 |
| isDedekindDomain canonical | 1 |
Description generation (PDg)
The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.
Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning. # Instructions Focus on describing the relationship, not the entities themselves. # Response Format Begin the description with \' Indicates...\'
Input
Predicate: isDedekindDomain
Generated description
Indicates that a ring is a Dedekind domain, meaning it is a Noetherian, integrally closed integral domain of Krull dimension one in which every nonzero ideal factors uniquely into prime ideals.
Sample triples (2)
| Subject | Object |
|---|---|
| Gaussian integers | true ⓘ |
| Hurwitz quaternions | true via predicate surface "hasUniqueFactorizationOfIdeals" ⓘ |