An **Euclidean domain** is an integral domain $R$ with a function
\[ \nu: R-\{0\}\to \Z_{\geq 0} \]
such that for all $a\in R$ and all $b\in R-\{0\}$, there exists $q,r\in R$ such that $a=bq+r$ and $r=0$ or $\nu(r)<\nu(b)$.

Euclidean domains are principal ideal domains, and hence, unique factorization domains.

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- Review status: reviewed
- Last edited by John Jones on 2019-03-20 10:37:05

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- 2019-03-20 10:37:05 by John Jones (Reviewed)