Euclidean domain
C6485
concept
A Euclidean domain is an integral domain equipped with a Euclidean function that allows a division algorithm, meaning any two elements can be written as a quotient and remainder with strictly smaller measure, enabling the construction of greatest common divisors via repeated division.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Euclidean domain canonical | 2 |
| Euclidean domain (as a 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: Euclidean domain
Generated description
A Euclidean domain is an integral domain equipped with a Euclidean function that allows a division algorithm, meaning any two elements can be written as a quotient and remainder with strictly smaller measure, enabling the construction of greatest common divisors via repeated division.
Instances (3)
| Instance | Via concept surface |
|---|---|
| Gaussian rationals ℚ(i) | Euclidean domain (as a field) |
| Gaussian integers | — |
| Hurwitz quaternions | — |