algebraic number field
C21313
concept
An algebraic number field is a finite field extension of the rational numbers, obtained by adjoining to ℚ a root of a nonzero polynomial with rational (or integer) coefficients.
All labels observed (3)
| Label | Occurrences |
|---|---|
| algebraic number field canonical | 2 |
| field extension | 2 |
| object in algebraic number theory | 2 |
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: algebraic number field
Generated description
An algebraic number field is a finite field extension of the rational numbers, obtained by adjoining to ℚ a root of a nonzero polynomial with rational (or integer) coefficients.
Instances (6)
| Instance | Via concept surface |
|---|---|
|
cyclotomic fields
surface form:
cyclotomic field
|
— |
| Gaussian rationals ℚ(i) | — |
| Noether field | field extension |
|
Galois
surface form:
Galois extension
|
field extension |
| Hilbert class field | object in algebraic number theory |
| Frobenius conjugacy class | object in algebraic number theory |