number field
C21312
concept
A number field is a finite-degree field extension of the rational numbers, typically obtained by adjoining to ℚ a root of a non-constant polynomial with rational (or integer) coefficients.
All labels observed (2)
| Label | Occurrences |
|---|---|
| number field canonical | 3 |
| number field extension | 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: number field
Generated description
A number field is a finite-degree field extension of the rational numbers, typically obtained by adjoining to ℚ a root of a non-constant polynomial with rational (or integer) coefficients.
Instances (4)
| Instance | Via concept surface |
|---|---|
|
cyclotomic fields
surface form:
cyclotomic field
|
— |
| Gaussian rationals ℚ(i) | — |
| Hilbert class field | number field extension |
|
CM fields
surface form:
CM field
|
— |