euclidean domain meaning in Hindi

Examples

1. This led to modern abstract algebraic notions such as Euclidean domains.
2. The unique factorization of Euclidean domains is useful in many applications.
3. The quadratic integer rings are helpful to illustrate Euclidean domains.
4. The rings for which such a theorem exists are called Euclidean domains.
5. This algorithm and the associated proof may also be extended to any Euclidean domain.
6. Again, the converse is not true : not every PID is a Euclidean domain.
7. All Euclidean domains are principal ideal domains.
8. Any Euclidean domain is a unique factorization domain ( UFD ), although the converse is not true.
9. Important examples are polynomial rings over the integers or over a field, Euclidean domains and principal ideal domains.
10. Examples of Euclidean domains include fields, polynomial rings in one variable over a field, and the Gaussian integers.