isNoetherianRing
P27197
predicate
Indicates that the ring satisfies the ascending chain condition on ideals, equivalently that every ideal is finitely generated.
All labels observed (4)
| Label | Occurrences |
|---|---|
| isNoetherianOn | 2 |
| inNoetherianCase | 1 |
| isNoetherian | 1 |
| isNoetherianRing 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: isNoetherianRing
Generated description
Indicates that the ring satisfies the ascending chain condition on ideals, equivalently that every ideal is finitely generated.
Sample triples (5)
| Subject | Object |
|---|---|
| Gaussian integers | true ⓘ |
| Weyl algebra | true via predicate surface "isNoetherian" ⓘ |
| Zariski topology | Spec(R) when R is Noetherian via predicate surface "isNoetherianOn" ⓘ |
| Zariski topology | varieties of finite type over a field via predicate surface "isNoetherianOn" ⓘ |
| Fitting ideal | finitely generated ideal via predicate surface "inNoetherianCase" ⓘ |