field
C21315
concept
A field is a mathematical structure consisting of a set equipped with two operations, addition and multiplication, that satisfy the usual arithmetic properties including commutativity, associativity, distributivity, and the existence of additive and multiplicative inverses for nonzero elements.
All labels observed (6)
| Label | Occurrences |
|---|---|
| field canonical | 3 |
| HRR field | 1 |
| fixed field | 1 |
| ghost field | 1 |
| local field | 1 |
| valued field | 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: field
Generated description
A field is a mathematical structure consisting of a set equipped with two operations, addition and multiplication, that satisfy the usual arithmetic properties including commutativity, associativity, distributivity, and the existence of additive and multiplicative inverses for nonzero elements.
Instances (7)
| Instance | Via concept surface |
|---|---|
| Gaussian rationals ℚ(i) | — |
| Noether field | fixed field |
| Fólkvangr | — |
| p-adic numbers | — |
| Levi-Civita field | valued field |
| Faddeev–Popov ghosts | ghost field |
|
Hutchinson–Rice–Rosengren singularity in fracture mechanics
surface form:
Hutchinson–Rice–Rosengren singularity
|
HRR field |