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| An Euclidean domain is an integral domain $D$ where an euclidean valuation $\nu$ has been defined. |
An Euclidean domain is an integral domain $D$ where an euclidean valuation $\nu$ has been defined. |
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| Any Euclidean domain is also a principal ideal domain and therefore also a unique factorization domain. |
Any Euclidean domain is also a principal ideal domain and therefore also a unique factorization domain. |
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| But even more important, on Euclidean domains we can define gcd and use Euclid's algorithm. |
But even more important, on Euclidean domains we can define gcd and use Euclid's algorithm. |
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| Examples of Euclidean domains are the rings $\Z$ and the polynomial ring on one variable $F[x]$ where $F$ is a field. |
Examples of Euclidean domains are the rings $\Z$ and the polynomial ring on one variable $F[x]$ where $F$ is a field. |
