Noetherian ring
C17814
concept
A Noetherian ring is a ring in which every ascending chain of ideals stabilizes, equivalently, every ideal is finitely generated.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Noetherian ring canonical | 2 |
| Dedekind domain | 1 |
| ring-theoretic property | 1 |
Description generation (CDg)
The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.
Instruction
generate a one-sentence description for a given conceptual class. # Response Format Return only the sentence: "Description: [one-sentence description of the conceptional class]"
Input
Class: Noetherian ring
Generated description
A Noetherian ring is a ring in which every ascending chain of ideals stabilizes, equivalently, every ideal is finitely generated.
Instances (4)
| Instance | Via concept surface |
|---|---|
| Weyl algebra | — |
|
Noetherian rings
surface form:
Noetherian ring
|
ring-theoretic property |
| Hurwitz quaternions | Dedekind domain |
| Cohen–Macaulay ring | — |