Euclidean Function

Definition: Euclidean Function

A Euclidean function on an Integral Domain $R$ is a function $f:R\setminus \{0\}\to {\mathbb{N}}_0$ such that for each $a,b\in R$, where $b\ne 0$, there exist $q,r\in R$ with $a=bq+r$ and either $r=0$ or $f(r)<f(b)$.